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The Stability Theorems for Subgroups of and

Published online by Cambridge University Press:  20 November 2018

Ali Lari-Lavassani  and
Yung-Chen Lu
Ali Lari-Lavassani
Affiliation:
Centre de Recherches Mathématiques, Université de Montréal CP 6128-A Montréal, Québec H3C 3J7
Yung-Chen Lu
Affiliation:
Department of Mathematics, The Ohio State University Columbus, Ohio 43210 U.S.A.
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Abstract

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In singularity theory, J. Damon gave elegant versions of the unfolding and determinacy theorems for geometric subgroups of . and . In this work, we propose a unified treatment of the smooth stability of germs and the structural stability of versai unfoldings for a large class of such subgroups.

Keywords

58C27singularity theorystabilityunfoldingstransversality
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 5 , 01 October 1994 , pp. 995 - 1006
Copyright
Copyright © Canadian Mathematical Society 1994

References

[AGV 85] Arnold, V. I., Gusein-Zade, S. M. and Varchenko, A. N., Singularities of Differentiable Maps, Vol. 1, Birkhäuser, Basel, Stuttgart, 1985.Google Scholar
[B 77] Bierstone, E., Generic equivariant maps, Real and Complex Singularities, Sijthoff and Nordhoff, 1977, 127–161.Google Scholar
[B 80] Bierstone, E., The Structure of Orbit Spaces and the Singularities of Equivariant Mappings, I.M.P.A., Rio de Janeiro, 1980.Google Scholar
[D 84] Damon, J., The unfolding and determinacy theorems for subgroups of and , Mem. Amer. Math. Soc. 306, Providence, Rhode Island, 1984.Google Scholar
[D 90] Damon, J., Private communications, 1990.Google Scholar
[G 84] Gervais, J. J., Deformations G-verselles et G-stables, Canad. J. Math. (1) 36(1984), 9–21.Google Scholar
[G 88] Gervais, J. J., Stability of Unfoldings in the Context of Equivariant Contact-Equivalence, Pacific J. Math. (2) 132(1988), 283–291.Google Scholar
[GSS 88] Golubitsky, M., Stewart, I. and Schaeffer, D. G., Singularity and Groups in Bifurcation Theory, Vol. 2, Springer-Verlag, Berlin, Heidelberg, New York, 1988.Google Scholar
[I 80] Izumiya, S., Stability of G-Unfoldings, Hokkaido Math. J. 9(1980), 36–45.Google Scholar
[LL 92] Lari-Lavassani, A. and Lu, Y.-C., On the stability of equivariant bifurcation problems and their unfoldings, Canad. Math. Bull. (2) 35(1992), 237–246.Google Scholar
[LL 93] Lari-Lavassani, A. and Lu, Y.-C., Equivariant Multiparameter Bifurcation Via Singularity Theory, J. Dynamics Differential Equations (2) 5(1993), 189–218.Google Scholar
[M 82] Martinet, J., Singularities of Smooth Functions and Maps, London Math. Soc. Lecture Note Ser. 58, Cambridge University Press, Cambridge, 1982.Google Scholar
[N 89] Nakai, I., Topological Stability Theorem for Composite Mappings, Ann. Inst. Fourier (2) 39(1989), 459–500.Google Scholar
[P, 1976] V. Poénaru, , Singularités C∞ en Présence de Symétrie, Lecture Notes in Math. 510, Springer-Verlag, Berlin, Heidelberg, New York, 1976.Google Scholar
[R 86] Roberts, M., Characterizations of finitely determined equivariant map germs, Math. Ann. 275(1986), 583–597.Google Scholar
[W 85] Wall, C. T. C., Equivariant Jets, Math. Ann. 272(1985), 41–65.Google Scholar
[W 74] Wasserman, G., Stability of unfoldings, Lecture Notes in Math. 510, Springer-Verlag, Berlin, Heidelberg, New York, 1974.Google Scholar
[W 75] Wasserman, G., Stability of unfoldings in space and time, Acta Math. 135(1975), 57–128.Google Scholar