[1] Ageev, O. 2005. The homogeneous spectrum problem in ergodic theory. Invent. Math., 160(2), 417–446.
[2] Ahern, P., and Gong, X. 2005. A complete classification for pairs of real analytic curves in the complex plane with tangential intersection. J. Dyn. Control Syst., 11(1), 1–71.
[3] Ahern, P., and O'Farrell, A. G. 2009. Reversible biholomorphic germs. Comput. Methods Funct. Theory, 9(2), 473–484.
[4] Alexander, H., and Wermer, J. 1998. Several complex variables and Banach al-gebras. Third edn. Graduate Texts in Mathematics, vol. 35. New York: Springer-Verlag.
[5] Allan, G. R. 2011. Introduction to Banach spaces and algebras. Oxford Graduate Texts in Mathematics, vol. 20. Oxford: Oxford University Press. Prepared for publication and with a preface by H. G., Dales.
[6] Anderson, R. D. 1962. On homeomorphisms as products of conjugates of a given homeomorphism and its inverse. Pages 231–234 of: Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961). Englewood Cliffs, N.J.: Prentice-Hall.
[7] Anzai, H. 1951. On an example of a measure preserving transformation which is not conjugate to its inverse. Proc. Japan Acad., 27, 517–522.
[8] Arnol′d, V. I. 1984. Reversible systems. Pages 1161–1174 of: Nonlinear and turbulent processes in physics, Vol. 3 (Kiev, 1983). Chur: Harwood Academic Publ.
[9] Arnol′d, V. I. 1988. Geometrical methods in the theory of ordinary differential equations. Second edn. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250. New York: Springer-Verlag. Translated from the Russian by J. M., Sziics.
[10] Arnol′d, V. I. 2006. Ordinary differential equations. Universitext. Berlin: Springer-Verlag. Translated from the Russian by Roger, Cooke, Second printing of the 1992 edition.
[11] Arnol′d, V. I., and Avez, A. 1968. Ergodic problems of classical mechanics. Translated from the French by A., Avez. W. A., Benjamin, Inc., New York-Amsterdam.
[12] Aschbacher, M. 1998. Near subgroups of finite groups. J. Group Theory, 1(2), 113–129.
[13] Aschbacher, M. 2000. Finite group theory. Second edn. Cambridge Studies in Advanced Mathematics, vol. 10. Cambridge: Cambridge University Press.
[14] Aschbacher, M., Meierfrankenfeld, U., and Stellmacher, B. 2001. Counting in-volutions. Illinois J. Math., 45(3), 1051–1060.
[15] Baake, M., and Roberts, J. A. G. 1997. Reversing symmetry group of Gl(2, Z) and PGl(2, Z) matrices with connections to cat maps and trace maps. J. Phys. A, 30(5), 1549–1573.
[16] Baake, M., and Roberts, J. A. G. 2001. Symmetries and reversing symmetries of toral automorphisms. Nonlinearity, 14(4), R1–R24.
[17] Baake, M., and Roberts, J. A. G. 2003. Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form. Phys. A, 317(1–2), 95–112.
[18] Baake, M., and Roberts, J. A. G. 2005. Symmetries and reversing symmetries of polynomial automorphisms of the plane. Nonlinearity, 18(2), 791–816.
[19] Baake, M., and Roberts, J. A. G. 2006. The structure of reversing symmetry groups. Bull. Austral. Math. Soc., 73(3), 445–459.
[20] Baake, M., Roberts, J. A. G., and Weiss, A. 2008. Periodic orbits of linear endomorphisms on the 2-torus and its lattices. Nonlinearity, 21(10), 2427–2446.
[21] Baake, M., Neumärker, N., and Roberts, J. A. G. 2013. Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices. Discrete Contin. Dyn. Syst., 33(2), 527–553.
[22] Bagiński, C. 1987. On sets of elements of the same order in the alternating group An. Publ. Math. Debrecen, 34(3–4), 313–315.
[23] Baker, A. 2002. Matrix groups. Springer Undergraduate Mathematics Series. London: Springer-Verlag London Ltd. An introduction to Lie group theory.
[24] Baker, I. N. 1961/1962. Permutable power series and regular iteration. J. Austral. Math. Soc., 2, 265–294.
[25] Baker, I. N. 1964. Fractional iteration near a fixpoint of multiplier 1. J. Austral. Math. Soc., 4, 143–148.
[26] Baker, I. N. 1967. Non-embeddable functions with a fixpoint of multiplier 1. Math. Z., 99, 377–384.
[27] Ballantine, C. S. 1977/78. Products of involutory matrices. I. Linear and Multi-linear Algebra, 5(1), 53–62.
[28] Beardon, A. F. 1983. The geometry of discrete groups. Graduate Texts in Mathematics, vol. 91. New York: Springer-Verlag.
[29] Bedford, T., Keane, M., and Series, C. (eds). 1991. Ergodic theory, symbolic dynamics, and hyperbolic spaces. Oxford Science Publications. New York: The Clarendon Press Oxford University Press. Papers from the Workshop on Hyperbolic Geometry and Ergodic Theory held in Trieste, April 17–28, 1989, Edited by T., Bedford, M., Keane and C., Series.
[30] Bessaga, C., and Pelczyinski, A. 1975. Selected topics in infinite-dimensional topology. Warsaw: PWN-Polish Scientific Publishers. Monografie Matematy-czne, Tom 58. [Mathematical Monographs, Vol. 58].
[31] Birkhoff, G. D. 1915. The restricted problem of three bodies. Rend. Circ. Mat. Palermo, 39, 265–334.
[32] Birkhoff, G. D. 1939. Déformations analytiques etfonctions auto-équivalentes. Ann. Inst. H. Poincare, 9, 51–122.
[33] Bishop, E. 1965. Differentiable manifolds in complex Euclidean space. Duke Math. J., 32, 1–21.
[34] Borevich, A. I., and Shafarevich, I. R. 1966. Number theory. Translated from the Russian by Newcomb, Greenleaf. Pure and Applied Mathematics, Vol. 20. New York: Academic Press.
[35] Botha, J. D. 2009. A unification of some matrix factorization results. Linear Algebra Appl., 431(10), 1719–1725.
[36] Brauer, R. 1963. Representations of finite groups. Pages 133–175 of: Lectures on Modern Mathematics, Vol. I. New York: Wiley.
[37] Brendle, T. E., and Farb, B. 2004. Every mapping class group is generated by 6 involutions. J. Algebra, 278(1), 187–198.
[38] Brin, M. G. 1996. The chameleon groups of Richard J. Thompson: automorphisms and dynamics. Inst. Hautes Etudes Sci. Publ. Math., 84, 5–33 (1997).
[39] Brin, M. G., and Squier, C. C. 1985. Groups of piecewise linear homeomor-phisms of the real line. Invent. Math., 79(3), 485–498.
[40] Brin, M. G., and Squier, C. C. 2001. Presentations, conjugacy, roots, and centralizers in groups of piecewise linear homeomorphisms of the real line. Comm. Algebra, 29(10), 4557–4596.
[41] Brucks, K. M., and Bruin, H. 2004. Topics from one-dimensional dynamics. London Mathematical Society Student Texts, vol. 62. Cambridge University Press, Cambridge.
[42] Buck, R. C. 1972. On approximation theory and functional equations. J. Ap-proximation Theory, 5, 228–237. Collection of articles dedicated to J. L., Walsh on his 75th birthday, III (Proc. Internat. Conf. Approximation Theory, Related Topics and their Applications, Univ. Maryland, College Park, Md., 1970).
[43] Bullett, S. 1988. Dynamics of quadratic correspondences. Nonlinearity, 1(1), 27–50.
[44] Bünger, F., Knüppel, F., and Nielsen, K. 1997. Products of symmetries in unitary groups. Linear Algebra Appl., 260, 9–42.
[45] Calica, A. B. 1971. Reversible homeomorphisms of the real line. Pacific J. Math., 39, 79–87.
[46] Camina, R. 2000. The Nottingham group. Pages 205–221 of: New horizons in pro-p groups. Progr. Math., vol. 184. Boston, MA: Birkhauser Boston.
[47] Cannon, J. W., Floyd, W. J., and Parry, W. R. 1996. Introductory notes on Richard Thompson's groups. Enseign. Math. (2), 42(3–4), 215–256.
[48] Carleson, L., and Gamelin, T. W. 1993. Complex dynamics. Universitext: Tracts in Mathematics. New York: Springer-Verlag.
[49] Cartan, H. 1995. Elementary theory of analytic functions of one or several complex variables. New York: Dover Publications Inc. Translated from the French, Reprint of the 1973 edition.
[50] Carter, R. W. 1972. Conjugacy classes in the Weyl group. Compositio Math., 25, 1–59.
[51] Cassels, J. W. S. 1978. Rational quadratic forms. London Mathematical Society Monographs, vol. 13. London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers].
[52] Chen, K-t. 1968. Normal forms of local diffeomorphisms on the real line. Duke Math. J., 35, 549–555.
[53] Cohn, H. 1978. A classical invitation to algebraic numbers and class fields. New York: Springer-Verlag. With two appendices by Olga Taussky: “Artin's 1932 Gottingen lectures on class field theory” and “Connections between algebraic number theory and integral matrices”, Universitext.
[54] Cohn, H. 1980. Advanced number theory. New York: Dover Publications Inc. Reprint of it A second course in number theory, 1962, Dover Books on Advanced Mathematics.
[55] Cohn, P. M. 2003. Basic algebra. London: Springer-Verlag London Ltd. Groups, rings and fields.
[56] Constantin, A., and Kolev, B. 1994. The theorem of Kerékjártó on periodic homeomorphisms of the disc and the sphere. Enseign. Math. (2), 40(3–4), 193204.
[57] Conway, J. H. 1997. The sensual (quadratic) form. Carus Mathematical Monographs, vol. 26. Washington, DC: Mathematical Association of America. With the assistance of Francis Y. C., Fung.
[58] Conway, J. H., and Sloane, N. J. A. 1999. Sphere packings, lattices and groups. Third edn. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290. New York: Springer-Verlag. With additional contributions by E. Bannai, R. E.Borcherds, J.Leech, S.P., Norton, A. M., Odlyzko, R. A., Parker, L., Queen and B. B., Venkov.
[59] Coxeter, H. S. M. 1947. The product of three reflections. Quart. Appl. Math., 5, 217–222.
[60] Coxeter, H. S. M. 1969. Introduction to geometry. Second edn. New York: John Wiley & Sons Inc.
[61] Coxeter, H. S. M. 1974. Regular complex polytopes. London: Cambridge University Press.
[62] Curtis, C. W. 1984. Linear algebra. Fourth edn. Undergraduate Texts in Mathematics. New York: Springer-Verlag. An introductory approach.
[63] de Melo, W., and van Strien, S. 1993. One-dimensional dynamics. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 25. Berlin: Springer-Verlag.
[64] de Paepe, P. J. 1986. Approximation on disks. Proc. Amer. Math. Soc., 97(2), 299–302.
[65] De Paepe, P. J. 2001. Eva Kallin's lemma on polynomial convexity. Bull. London Math. Soc., 33(1), 1–10.
[66] Devaney, R. L. 1976. Reversible diffeomorphisms and flows. Trans. Amer. Math. Soc., 218, 89–113.
[67] Dieudonné, J. 1951. On the automorphisms of the classical groups. With a sup-plement by Loo-Keng Hua. Mem. Amer. Math. Soc., 1951(2), vi+122.
[68] Dijkstra, J. J., and van Mill, J. 2006. On the group of homeomorphisms of the real line that map the pseudoboundary onto itself. Canad. J. Math., 58(3), 529–547.
[69] Diliberto, S. P., and Straus, E. G. 1951. On the approximation of a function of several variables by the sum of functions of fewer variables. Pacific J. Math., 1, 195–210.
[70] Djoković, D. Ž. 1967. Product of two involutions. Arch. Math. (Basel), 18, 582–584.
[71] Djoković, D. Ž. 1986. Pairs of involutions in the general linear group. J. Algebra, 100(1), 214–223.
[72] Djoković, D. Ž., and Malzan, J. G. 1982. Products of reflections in U(p, q). Mem. Amer. Math. Soc., 37(259), vi+82.
[73] Écalle, J. 1975. Théorie itérative: introduction a latheorie des invariants holomorphes. J. Math. Pures Appl. (9), 54, 183–258.
[74] Eisenbud, D., Hirsch, U., and Neumann, W. 1981. Transverse foliations of Seifert bundles and self-homeomorphism of the circle. Comment. Math. Helv., 56(4), 638–660.
[75] Ellers, E. W. 1977. Bireflectionality in classical groups. Canad. J. Math., 29(6), 1157–1162.
[76] Ellers, E. W. 1983. Cyclic decomposition of unitary spaces. J. Geom., 21(2), 101–107.
[77] Ellers, E. W. 1993. The reflection length of a transformation in the unitary group over a finite field. Linear and Multilinear Algebra, 35(1), 11–35.
[78] Ellers, E. W. 1999. Bireflectionality of orthogonal and symplectic groups of characteristic 2. Arch. Math. (Basel), 73(6), 414–418.
[79] Ellers, E. W. 2004. Conjugacy classes of involutions in the Lorentz group Q(V) and in SO(V). Linear Algebra Appl., 383, 77–83.
[80] Ellers, E. W., and Malzan, J. 1990. Products of reflections in the kernel of the spinorial norm. Geom. Dedicata, 36(2–3), 279–285.
[81] Ellers, E. W., and Nolte, W. 1982. Bireflectionality of orthogonal and symplectic groups. Arch. Math. (Basel), 39(2), 113–118.
[82] Ellers, E. W., and Villa, O. 2004. The special orthogonal group is trireflectional. Arch. Math. (Basel), 82(2), 122–127.
[83] Engel, K-J., and Nagel, R. 2000. One-parameter semigroups for linear evolution equations. Graduate Texts in Mathematics, vol. 194. New York: Springer-Verlag. With contributions by S., Brendle, M., Campiti, T., Hahn, G., Metafune, G., Nickel, D., Pallara, C., Perazzoli, A., Rhandi, S., Romanelli and R., Schnaubelt.
[84] Falcolini, C. 2002. Collisions and singularities in the n-body problem. Lecture Notes in Physics, vol. 590. Berlin: Springer-Verlag. Edited by D., Benest and C., Froeschlé.
[85] Fein, B. 1970. A note on the Brauer-Speiser theorem. Proc. Amer. Math. Soc., 25, 620–621.
[86] Feit, W. 1967. Characters of finite groups. W.A., Benjamin, Inc., New York-Amsterdam.
[87] Feit, W., and Thompson, J. G. 1963. Solvability of groups of odd order. Pacific J. Math., 13, 775–1029.
[88] Feit, W., and Zuckerman, G. J. 1982. Reality properties of conjugacy classes in spin groups and symplectic groups. Pages 239–253 of: Algebraists' homage: papers in ring theory and related topics (New Haven, Conn., 1981). Contemp. Math., vol. 13. Providence, R.I.: Amer. Math. Soc.
[89] Fine, N. J., and Schweigert, G. E. 1955. On the group of homeomorphisms of an arc. Ann. of Math. (2), 62, 237–253.
[90] Foguel, T., Kinyon, M. K., and Phillips, J. D. 2006. On twisted subgroups and Bol loops of odd order. Rocky Mountain J. Math., 36(1), 183–212.
[91] Foreman, M., Rudolph, D. J., and Weiss, B. 2011. The conjugacy problem in ergodic theory. Ann. of Math. (2), 173(3), 1529–1586.
[92] Forstnerič, F. 1992. A smooth holomorphically convex disc in C2 that is not locally polynomially convex. Proc. Amer. Math. Soc., 116(2), 411–415.
[93] Gal′t, A. A. 2010. Strongly real elements in finite simple orthogonal groups. Sibirsk. Mat. Zh., 51(2), 241–248.
[94] Gamkrelidze, R. V. (ed). 1990. Several complex variables. I. Encyclopaedia of Mathematical Sciences, vol. 7. Berlin: Springer-Verlag. Introduction to complex analysis, A translation of Sovremennye problemy matematiki. Fundamentalnye napravleniya, Tom 7, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. In-form., Moscow, 1985 [MR0850489 (87f:32003)], Translation by P. M., Gauthier, Translation edited by A. G., Vitushkin.
[95] Gauss, C. F. 1986. Disquisitiones arithmeticae. New York: Springer-Verlag. Translated and with a preface by Arthur A., Clarke, Revised by William C., Wa-terhouse, Cornelius Greither and A. W., Grootendorst and with a preface by Waterhouse.
[96] Ghys, É. 2001. Groups acting on the circle. Enseign. Math. (2), 47(3–4), 329–407.
[97] Ghys, É., and Sergiescu, V. 1980. Stabilite et conjugaison differentiable pour certains feuilletages. Topology, 19(2), 179–197.
[98] Giblin, J., and Markovic, V. 2006. Classification of continuously transitive circle groups. Geom. Topol., 10, 1319–1346.
[99] Gill, N., and Short, I. 2010. Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequationes Math., 79(1–2), 23–37.
[100] Gill, N., and Singh, A. 2011a. Real and strongly real classes in PGLn(q) and quasi-simple covers of PSLn(q). J. Group Theory, 14, 461–489.
[101] Gill, N., and Singh, A. 2011b. Real and strongly real classes in SLn (q). J. Group Theory, 14, 437–459.
[102] Gill, N., O'Farrell, A. G., and Short, I. 2009. Reversibility in the group of homeomorphisms of the circle. Bull. Lond. Math. Soc., 41(5), 885–897.
[103] Gómez, A., and Meiss, J. D. 2003. Reversible polynomial automorphisms of the plane: the involutory case. Phys. Lett. A, 312(1–2), 49–58.
[104] Gómez, A., and Meiss, J. D. 2004. Reversors and symmetries for polynomial automorphisms of the complex plane. Nonlinearity, 17(3), 975–1000.
[105] Gongopadhyay, K. 2011. Conjugacy classes in Möbius groups. Geom. Dedicata, 151, 245–258.
[106] Gongopadhyay, K., and Parker, J. R. 2012. Reversible complex hyperbolic isometries. Preprint.
[107] Goodson, G., and Lemannczyk, M. 1996. Transformations conjugate to their inverses have even essential values. Proc. Amer. Math. Soc., 124(9), 2703–2710.
[108] Goodson, G. R. 1996. The structure of ergodic transformations conjugate to their inverses. Pages 369–385 of: Ergodic theory of Zd actions (Warwick, 1993–1994). London Math. Soc. Lecture Note Ser., vol. 228. Cambridge: Cambridge Univ. Press.
[109] Goodson, G. R. 1997. The inverse-similarity problem for real orthogonal matrices. Amer. Math. Monthly, 104(3), 223–230.
[110] Goodson, G. R. 1999. Inverse conjugacies and reversing symmetry groups. Amer. Math. Monthly, 106(1), 19–26.
[111] Goodson, G. R. 2000a. Conjugacies between ergodic transformations and their inverses. Colloq. Math., 84/85(, part 1), 185–193. Dedicated to the memory of Anzelm Iwanik.
[112] Goodson, G. R. 2000b. The converse of the inverse-conjugacy theorem for unitary operators and ergodic dynamical systems. Proc. Amer. Math. Soc., 128(5), 1381–1388.
[113] Goodson, G. R. 2002. Ergodic dynamical systems conjugate to their composition squares. Acta Math. Univ. Comenian. (N.S.), 71(2), 201–210.
[114] Goodson, G. R. 2010. Groups having elements conjugate to their squares and connections with dynamical systems. Applied Mathematics, 1, 416–424.
[115] Goodson, G. R., del Junco, A., Lemańczyk, M., and Rudolph, D. J. 1996. Ergodic transformations conjugate to their inverses by involutions. Ergodic Theory Dynam. Systems, 16(1), 97–124.
[116] Goodson, Geoffrey R. 2007. Spectral properties of ergodic dynamical systems conjugate to their composition squares. Colloq. Math., 107(1), 99–118.
[117] Gorenstein, D. 1968. Finite groups. New York: Harper & Row Publishers.
[118] Gow, R. 1975. Real-valued characters of solvable groups. Bull. London Math. Soc., 7, 132.
[119] Gow, R. 1976. Real-valued characters and the Schur index. J. Algebra, 40(1), 258–270.
[120] Gow, R. 1979. Real-valued and 2-rational group characters. J. Algebra, 61(2), 388–413.
[121] Gow, R. 1981. Products of two involutions in classical groups of characteristic 2. J. Algebra, 71(2), 583–591.
[122] Gow, R. 1988. Commutators in the symplectic group. Arch. Math. (Basel), 50(3), 204–209.
[123] Graham, D., Keane, S., and O'Farrell, A. G. 2001. Simeadracht amchulaithe chorais dinimiciuil. in: R.N., Shorten, T., Ward and T., Lysaght (eds), Proceedings of the Irish Systems and Signals Conference, 27–31. Translation available online from AOF.
[124] Guba, V., and Sapir, M. 1997. Diagram groups. Mem. Amer. Math. Soc., 130(620), viii+117.
[125] Gustafson, W. H. 1991. On products of involutions. Pages 237–255 of: Paul Halmos. New York: Springer.
[126] Gustafson, W. H., Halmos, P. R., and Radjavi, H. 1976. Products of involutions. Linear Algebra andAppl., 13(1/2), 157–162. Collection of articles dedicated to Olga Taussky Todd.
[127] Halmos, P. R., and von Neumann, J. 1942. Operator methods in classical me-chanics. II. Ann. of Math. (2), 43, 332–350.
[128] Hamkins, J. D. 1998. Every group has a terminating transfinite automorphism tower. Proc. Amer. Math. Soc., 126(11), 3223–3226.
[129] Higman, G. 1974. Finitely presented infinite simple groups. Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra. Notes on Pure Mathematics, No. 8 (1974).
[130] Hillar, C. J., and Rhea, D. L. 2007. Automorphisms of finite abelian groups. Amer. Math. Monthly, 114(10), 917–923.
[131] Hirsch, M. W., and Smale, S. 1974. Differential equations, dynamical systems, and linear algebra. Academic Press [A subsidiary of Harcourt Brace Jo-vanovich, Publishers], New York-London. Pure and Applied Mathematics, Vol. 60.
[132] Hjorth, G. 2000. Classification and orbit equivalence relations. Mathematical Surveys and Monographs, vol. 75. Providence, RI: American Mathematical Society.
[133] Hladnik, M., Omladic, M., and Radjavi, H. 2001. Products of roots of the identity. Proc. Amer. Math. Soc., 129(2), 459–465.
[134] Hoffman, F., and Paige, E. C. 1970/1971. Products of two involutions in the general linear group. Indiana Univ. Math. J., 20, 1017–1020.
[135] Huang, X. 1998. On an n-manifold in Cn near an elliptic complex tangent. J. Amer. Math. Soc., 11(3), 669–692.
[136] Huang, X. J., and Krantz, S. G. 1995. On a problem of Moser. Duke Math. J., 78(1), 213–228.
[137] Il′yashenko, Yu. S. 1993. Nonlinear Stokes phenomena. Pages 1–55 of: Nonlinear Stokes phenomena. Adv. Soviet Math., vol. 14. Providence, RI: Amer. Math. Soc.
[138] Isaacs, I. M. 1976. Character theory of finite groups. New York: Academic Press [Harcourt Brace Jovanovich Publishers]. Pure and Applied Mathematics, No. 69.
[139] Ishibashi, H. 1995. Involutary expressions for elements in GLn(Z) and SLn(Z). Linear Algebra Appl., 219, 165–177.
[140] James, G., and Liebeck, M. 2001. Representations and characters of groups. Second edn. New York: Cambridge University Press.
[141] Jarczyk, W. 2002. Reversible interval homeomorphisms. J. Math. Anal. Appl., 272(2), 473–479.
[142] Jordan, C. R., Jordan, D. A., and Jordan, J. H. 2002. Reversible complex Henon maps. Experiment. Math., 11(3), 339–347.
[143] Kasner, E. 1915. Conformal classification of analytic arcs or elements: Poincaré's local problem of conformal geometry. Trans. Amer. Math. Soc., 16(3), 333–349.
[144] Kasner, E. 1916. Infinite Groups Generated by Conformal Transformations of Period Two (Involutions and Symmetries). Amer. J. Math., 38(2), 177–184.
[145] Katok, A., and Hasselblatt, B. 1995. Introduction to the modern theory of dynamical systems. Encyclopedia of Mathematics and its Applications, vol. 54. Cambridge: Cambridge University Press. With a supplementary chapter by Katok and Leonardo Mendoza.
[146] Kaur, D., and Kulsherstha, A.Strongly real special 2-groups. To appear.
[147] Kenig, C. E., and Webster, S. M. 1982. The local hull of holomorphy of a surface in the space of two complex variables. Invent. Math., 67(1), 1–21.
[148] Khavinson, S. Ya. 1995. The annihilator of linear superpositions. Algebra i Analiz, 7(3), 1–42.
[149] Knüppel, F. 1988. Products of involutions in orthogonal groups. Pages 231–247 of: Combinatorics '86 (Trento, 1986). Ann. Discrete Math., vol. 37. Amsterdam: North-Holland.
[150] Knüppel, F., and Nielsen, K. 1987a. On products of two involutions in the orthogonal group of a vector space. Linear Algebra Appl., 94, 209–216.
[151] Knüppel, F., and Nielsen, K. 1987b. Products of involutions in O+(V). Linear Algebra Appl., 94, 217–222.
[152] Knüppel, F., and Nielsen, K. 1991. SL(V) is 4-reflectional. Geom. Dedicata, 38(3), 301–308.
[153] Knüppel, F., and Thomsen, G. 1998. Involutions and commutators in orthogonal groups. J. Austral. Math. Soc. Ser. A, 65(1), 1–36.
[154] Kolesnikov, S. G., and Nuzhin, Ja. N. 2005. On strong reality of finite simple groups. Acta Appl. Math., 85(1–3), 195–203.
[155] Kopell, N. 1970. Commuting diffeomorphisms. Pages 165–184 of: Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968). Providence, R.I.: Amer. Math. Soc.
[156] Korkmaz, M. 2005. On stable torsion length of a Dehn twist. Math. Res. Lett., 12(2–3), 335–339.
[157] Kuczma, M., Choczewski, B., and Ger, R. 1990. Iterative functional equations. Encyclopedia of Mathematics and its Applications, vol. 32. Cambridge: Cambridge University Press.
[158] Laffey, T. J. 1997. Lectures on integer matrices. Unpublished lecture notes.
[159] Lamb, J. S. W. 1992. Reversing symmetries in dynamical systems. J. Phys. A, 25(4), 925–937.
[160] Lamb, J. S. W. 1995. Resonant driving and k-symmetry. Phys. Lett. A, 199(1–2), 55–60.
[161] Lamb, J. S. W. 1996. Area-preserving dynamics that is not reversible. Phys. A, 228(1–4), 344–365.
[162] Lamb, J. S. W., and Quispel, G. R. W. 1994. Reversing k-symmetries in dynamical systems. Phys. D, 73(4), 277–304.
[163] Lamb, J. S. W., and Quispel, G. R. W. 1995. Cyclic reversing k-symmetry groups. Nonlinearity, 8(6), 1005–1026.
[164] Lamb, J. S. W., and Roberts, J. A. G. 1998. Time-reversal symmetry in dynamical systems: a survey. Phys. D, 112(1–2), 1–39. Time-reversal symmetry in dynamical systems (Coventry, 1996).
[165] Lamb, J. S. W., Roberts, J. A. G., and Capel, H. W. 1993. Conditions for local (reversing) symmetries in dynamical systems. Phys. A, 197(3), 379–422.
[166] Lávička, R., O'Farrell, A. G., and Short, I. 2007. Reversible maps in the group of quaternionic Möbius transformations. Math. Proc. Cambridge Philos. Soc., 143(1), 57–69.
[167] Lewis Jr., D. C. 1961. Reversible transformations. Pacific J. Math., 11, 1077–1087.
[168] Liebeck, M. W., O'Brien, E. A., Shalev, A., and Tiep, P. H. 2010. The Ore conjecture. J. Eur. Math. Soc. (JEMS), 12(4), 939–1008.
[169] Liu, K. M. 1988a. Decomposition of matrices into three involutions. Linear Algebra Appl., 111, 1–24.
[170] Liu, K. M. 1988b. Decomposition of matrices into three involutions. Linear Algebra Appl., 111, 1–24.
[171] Liverpool, L. S. O. 1974/75. Fractional iteration near a fix point of multiplier 1. J. London Math. Soc. (2), 9, 599–609.
[172] Lubin, J. 1994. Non-Archimedean dynamical systems. Compositio Math., 94(3), 321–346.
[173] MacKay, R. S. 1993. Renormalisation in area-preserving maps. Advanced Series in Nonlinear Dynamics, vol. 6. River Edge, NJ: World Scientific Publishing Co. Inc.
[174] Malgrange, B. 1982. Travaux d'Écalle et de Martinet-Ramis sur les systemes dynamiques. Pages 59–73 of: Bourbaki Seminar, Vol. 1981/1982. Astérisque, vol. 92. Paris: Soc. Math. France.
[175] Markley, N. G. 1970. Homeomorphisms of the circle without periodic points. Proc. London Math. Soc. (3), 20, 688–698.
[176] Marshall, D. E., and O'Farrell, A. G. 1979. Uniform approximation by real functions. Fund. Math., 54, 203–11.
[177] Marshall, D. E., and O'Farrell, A. G. 1983. Approximation by a sum of two algebras. The lightning bolt principle. J. Funct. Anal., 52(3), 353–368.
[178] Mazurov, V. D., and Khukhro, E. I. (eds). 2014. The Kourovka notebook. Eighteenth edn. Novosibirsk: Russian Academy of Sciences Siberian Division Institute of Mathematics. Unsolved problems in group theory, Including archive of solved problems.
[179] McCarthy, P. J., and Stephenson, W. 1985. The classification of the conjugacy classes of the full group of homeomorphisms of an open interval and the general solution of certain functional equations. Proc. London Math. Soc. (3), 51(1), 95–112.
[180] McCleary, S. H. 1978. Groups of homeomorphisms with manageable automorphism groups. Comm. Algebra, 6(5), 497–528.
[181] Medvedev, V. A. 1992. Refutation of a theorem of Diliberto and Straus. Mat. Zametki, 51(4), 78–80, 142.
[182] Meyerson, M. D. 1981. Every power series is a Taylor series. Amer. Math. Monthly, 88(1), 51–52.
[183] MillerIII, C. F. III, C. F. 1971. On group-theoretic decision problems and their classification. Princeton, N.J.: Princeton University Press. Annals of Mathematics Studies, No. 68.
[184] Moser, J. K., and Webster, S. M. 1983. Normal forms for real surfaces in C2 near complex tangents and hyperbolic surface transformations. Acta Math., 150(3–4), 255–296.
[185] Muckenhoupt, B. 1961. Automorphisms of formal power series under substitution. Trans. Amer. Math. Soc., 99, 373–383.
[186] Nakai, I. 1998. The classification of curvilinear angles in the complex plane and the groups of ± holomorphic diffeomorphisms. Ann. Fac. Sci. Toulouse Math. (6), 7(2), 313–334.
[187] Navas, A. 2007. Grupos de difeomorfismos del círculo. Ensaios Matemáticos [Mathematical Surveys], vol. 13. Rio de Janeiro: Sociedade Brasileira de Matematica.
[188] O'Farrell, A. G. 2004. Conjugacy, involutions, and reversibility for real homeomorphisms. Irish Math. Soc. Bull., 54, 41–52.
[189] O'Farrell, A. G. 2008. Composition of involutive power series, and reversible series. Comput. Methods Funct. Theory, 8(1–2), 173–193.
[190] O'Farrell, A. G., and Roginskaya, M. 2010. Conjugacy of real diffeomorphisms. Asurvey. Algebra i Analiz, 22(1), 3–56.
[191] O'Farrell, A. G., and Sanabria-Garcia, M.A. 2002. De Paepe's disc has nontrivial polynomial hull. Bull. LMS, 34, 490–494.
[192] O'Farrell, A. G., and Short, I. 2009. Reversibility in the diffeomorphism group of the real line. Publ. Mat., 53(2), 401–415.
[193] O'Farrell, A. G., and Zaitsev, D.Formally-reversible maps of (ℂ2,0). To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), DOI:10.2422/2036–2145.201201_001.
[194] O'Farrell, A. G., and Zaitsev, D. 2014. Factoring formal maps into reversible or involutive factors. J. Algebra, 399, 657–674.
[195] Pérez Marco, R. 1995. Nonlinearizable holomorphic dynamics having an uncountable number of symmetries. Invent. Math., 119(1), 67–127.
[196] Poincaré, H. 1907. Les fonctions analytiques de deux variables et la prepresentation conforme. Rend. Circ. Mat. Palermo, 23(1), 185–220.
[197] Poincaré, H. 1996. Œuvres. Tome VI. Les Grands Classiques Gauthier-Villars. [Gauthier-Villars Great Classics]. Sceaux: Éditions Jacques Gabay. Géométrie. Analysis situs (topologie). [Geometry. Analysis situs (topology)], Reprint of the 1953 edition.
[198] Quispel, G. R. W., and Capel, H. W. 1989. Local reversibility in dynamical systems. Phys. Lett. A, 142(2–3), 112–116.
[199] Quispel, G. R. W., and Roberts, J. A. G. 1988. Reversible mappings of the plane. Phys. Lett. A, 132(4), 161–163.
[200] Radjavi, H. 1975. Decomposition of matrices into simple involutions. Linear Algebra and Appl., 12(3), 247–255.
[201] Radjavi, H. 1981. The group generated by involutions. Proc. Roy. Irish Acad. Sect. A, 81(1), 9–12.
[202] Rämö, J. 2011. Strongly real elements of orthogonal groups in even characteristic. J. Group Theory, 14(1), 9–30.
[203] Ratcliffe, J. G. 1994. Foundations of hyperbolic manifolds. Graduate Texts in Mathematics, vol. 149. New York: Springer-Verlag.
[204] Roberts, J. A. G., and Capel, H. W. 1992. Area preserving mappings that are not reversible. Phys. Lett. A, 162(3), 243–248.
[205] Roberts, J. A. G., and Quispel, G. R. W. 1992. Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems. Phys. Rep., 216(2–3), 63–177.
[206] Robinson, D. J. S. 1996. A course in the theory of groups. Second edn. Graduate Texts in Mathematics, vol. 80. New York: Springer-Verlag.
[207] Sarnak, P. 2007. Reciprocal geodesics. Pages 217–237 of: Analytic number theory. Clay Math. Proc., vol. 7. Providence, RI: Amer. Math. Soc.
[208] Schreier, J., and Ulam, S. 1933. Über die Permutationsgruppe der naturlichen Zahlenfolge. StudiaMath., 4, 134–141.
[209] Sepanski, M. R. 2007. Compact Lie groups. Graduate Texts in Mathematics, vol. 235. New York: Springer.
[210] Series, C. 1985. The geometry of Markoff numbers. Math. Intelligencer, 7(3), 20–29.
[211] Sevryuk, M. B. 1986. Reversible systems. Lecture Notes in Mathematics, vol. 1211. Berlin: Springer-Verlag.
[212] Shalev, Aner. 2009. Word maps, conjugacy classes, and a noncommutative Waring-type theorem. Ann. of Math. (2), 170(3), 1383–1416.
[213] Short, I. 2008. Reversible maps in isometry groups of spherical, Euclidean and hyperbolic space. Math. Proc. R. Ir. Acad., 108(1), 33–46.
[214] Siegel, C. B., and Moser, J. K. 1995. Lectures on Celestial Mechanics, reprint of the 1971 edition. Berlin, Heidelberg: Springer.
[215] Simon, B. 1996. Representations of finite and compact groups. Graduate Studies in Mathematics, vol. 10. Providence, RI: American Mathematical Society.
[216] Singh, A., and Thakur, M. 2005. Reality properties of conjugacy classes in G2. Israel J. Math., 145, 157–192.
[217] Singh, A., and Thakur, M. 2008. Reality properties of conjugacy classes in algebraic groups. Israel J. Math., 165, 1–27.
[218] Springer, T. A. 1974. Regular elements of finite reflection groups. Invent. Math., 25, 159–198.
[219] Stebe, P. F. 1972. Conjugacy separability of groups of integer matrices. Proc. Amer. Math. Soc., 32, 1–7.
[220] Sternberg, S. 1957. Local Cn transformations of the real line. Duke Math. J., 24, 97–102.
[221] Sternfeld, Y. 1986. Uniform separation of points and measures and representation by sums of algebras. Israel J. Math., 55(3), 350–362.
[222] Stewart, I., and Tall, D. 1979. Algebraic number theory. London: Chapman and Hall. Chapman and Hall Mathematics Series.
[223] Szekeres, G. 1964. Fractional iteration of entire and rational functions. J. Austral. Math. Soc., 4, 129–142.
[224] Takens, F. 1973. Normal forms for certain singularities of vectorfields. Ann. Inst. Fourier (Grenoble), 23(2), 163–195. Colloque International sur l'Analyse et la Topologie Differentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972).
[225] Taylor, D. E. 1992. The geometry of the classical groups. Sigma Series in Pure Mathematics, vol. 9. Berlin: Heldermann Verlag.
[226] Thomas, S.The automorphism tower problem. Book in preparation.
[227] Thomas, S. 1985. The automorphism tower problem. Proc. Amer. Math. Soc., 95(2), 166–168.
[228] Thompson, R. C. 1961. Commutators in the special and general linear groups. Trans. Amer. Math. Soc., 101, 16–33.
[229] Thompson, R. C. 1962a. Commutators of matrices with coefficients from the field of two elements. Duke Math. J., 29, 367–373.
[230] Thompson, R. C. 1962b. On matrix commutators. Portugal. Math., 21, 143–153.
[231] Tiep, P. H., and Zalesski, A. E. 2005. Real conjugacy classes in algebraic groups and finite groups of Lie type. J. Group Theory, 8(3), 291–315.
[232] Trépreau, J-M. 2003. Discrimination analytique des difféomorphismes résonnants de (ℂ,0) et réflexion de Schwarz. Astérisque, 271–319. Autour de l'analyse microlocale.
[233] Vdovin, E. P., and Gal′t, A. A. 2010. Strong reality of finite simple groups. Sibirsk. Mat. Zh., 51(4), 769–777.
[234] Villa, O. 2003. An example of a bireflectional spin group. Arch. Math. (Basel), 81(1), 1–4.
[235] Vinroot, C. R. 2004. A factorization in GSp(V). Linear Multilinear Algebra, 52(6), 385–403.
[236] Voronin, S. M. 1981. Analytic classification of germs of conformal mappings (C, 0) → (C, 0). Funktsional. Anal. i Prilozhen., 15(1), 1–17, 96.
[237] Voronin, S. M. 1982. Analytic classification of pairs of involutions and its applications. Funktsional. Anal. i Prilozhen., 16(2), 21–29, 96.
[238] Wall, G. E. 1963. On the conjugacy classes in the unitary, symplectic and orthogonal groups. J. Austral. Math. Soc., 3, 1–62.
[239] Walsh, J. A. 1999. The dynamics of circle homeomorphisms: a hands-on introduction. Math. Mag., 72(1), 3–13.
[240] Webster, S. M. 1996. Double valued reflection in the complex plane. Enseign. Math. (2), 42(1–2), 25–48.
[241] Webster, S. M. 1997. A note on extremal discs and double valued reflection. Pages 271–276 of: Multidimensional complex analysis and partial differential equations (Sao Carlos, 1995). Contemp. Math., vol. 205. Providence, RI: Amer. Math. Soc.
[242] Webster, S. M. 1998. Real ellipsoids and double valued reflection in complex space. Amer. J. Math., 120(4), 757–809.
[243] Weyl, H. 1997. The classical groups. Princeton Landmarks in Mathematics. Princeton, NJ: Princeton University Press. Their invariants and representations, Fifteenth printing, Princeton Paperbacks.
[244] Whittaker, J. V. 1963. On isomorphic groups and homeomorphic spaces. Ann. of Math. (2), 78, 74–91.
[245] Wiegerinck, J. 1995. Local polynomially convex hulls at degenerated CR singularities of surfaces in C2. Indiana Univ. Math. J., 44(3), 897–915.
[246] Wilson, R., Walsh, P., Tripp, J., Suleiman, I., Parker, R., Norton, S., Nickerson, S., Linton, S., Bray, J., and Abbott, R.ATLAS of finitie group representations – Version3. http://brauer.maths.qmul.ac.uk/Atlas/v3/.
[247] Wonenburger, M. J. 1966. Transformations which are products of two involutions. J. Math. Mech., 16, 327–338.
[248] Xia, Z. 1992. The existence of noncollision singularities in Newtonian systems. Ann. of Math. (2), 135(3), 411–468.
[249] Yale, P. B. 1966. Automorphisms of the complex numbers. Math. Magazine, 39, 135–141.
[250] Yoccoz, J.-C. 1995. Petits diviseurs en dimension 1. Paris: Société Mathématique de France. Astérisque No. 231 (1995).
[251] Young, S. W. 1994. The representation of homeomorphisms on the interval as finite compositions of involutions. Proc. Amer. Math. Soc., 121(2), 605–610.
