Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-31T09:50:26.928Z Has data issue: false hasContentIssue false
  • English
  • Français

Growth rate of surface homeomorphisms and flow equivalence

Published online by Cambridge University Press:  19 September 2008

David Fried
David Fried
Affiliation:
Mathematics Department, Boston University, Boston, Mass. 02215, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study which algebraic integers λ ≥ l arise as the growth rate of a mapping class of a surface and give conditions that are necessary and perhaps sufficient. Flow equivalence and twisted Lefschetz zeta functions are used to generate families of λ's. Examples and open problems are included

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 4 , December 1985 , pp. 539 - 563
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[AY]Arnoux, P. & Yoccoz, J. C.. Construction de diffeomorphisme pseudo-Anosov. C.R. Acad. Sci. Paris 292 (1981), 75–78.Google Scholar
[BR]Banchoff, T. & Rosen, M.. Periodic points of Anosov diffeomorphisms. In Global Analysis XIV, Proc. Symp. Pure Math. Amer. Math. Soc: Providence, 1970.CrossRefGoogle Scholar
[B]Birkhoff, G. D.. Dynamical systems with 2 degrees of freedom. Trans. Amer. Math. Soc. 18 (1917), 199–300.CrossRefGoogle Scholar
[Bo]Bowen, R.. Entropy and the fundamental group. Springer Lecture Notes in Maths 668, New York, 1978.CrossRefGoogle Scholar
[FLP]Fathi, A., Laudenbach, F. & Poenaru, V., (eds). Travaux de Thurston sur les Surfaces. Asterisque 66–67 (1979).Google Scholar
[FS]Fathi, A. & Shub, M.. Some dynamics of pseudo-Anosov diffeomorphisms. In [FLP], op. cit.Google Scholar
[Fr]Franks, J.. Homology and Dynamical Systems. CBMS Reg. Conf. Series 49. Amer. Math. Soc: Providence, 1982.CrossRefGoogle Scholar
[Fl]Fried, D.. Geometry of cross-sections to flows. Topology 21 (1982), 353–371.CrossRefGoogle Scholar
[F2]Fried, D.. Fibrations with pseudo-Anosov monodromy. In [FLP], op. cit.Google Scholar
[F3]Fried, D.. Flow equivalence, hyperbolic systems and a new zeta function for flows. Comm. Math. Helv. 57 (1982), 237–259.CrossRefGoogle Scholar
[F4]Fried, D.. Homological identities for closed orbits. Inv. Math. 71, 419–442 (1983).CrossRefGoogle Scholar
[F5]Fried, D.. Periodic points and twisted coefficients. In Geometric Dynamics, Proceedings of 1981 IMPA Symposium on Dynamical Systems. Springer Lecture Notes in Maths 1007, 261–293.Google Scholar
[F6]Fried, D.. Entropy and twisted cohomology. Preprint.Google Scholar
[F7]Fried, D.. Monodromy and dynamical systems. IHES preprint, 07 1983.Google Scholar
[F8]Fried, D.. Efficiency vs. hyperbolicity on tori. In Global Theory of Dynamical Systems, Springer Lecture Notes in Maths. 819.Google Scholar
[F9]Fried, D.. Transitive Anosov flows and pseudo-Anosov maps. Topology, 22 (1983), 299–303.CrossRefGoogle Scholar
[F10]Fried, D.. Subshifts on surfaces. Ergod. Th. & Dynam. Sys. 2 (1982), 15–21.CrossRefGoogle Scholar
[I]Ikegami, G.. Flow equivalence of diffeomorphisms. Osaka J. Math. 8 (1971), 49–70; 9 (1972), 335–336.Google Scholar
[L]Ljunggren, W.. On the irreducibility of certain trinomials and quadrinomials. Math. Scand. 8 (1960), 65–70.CrossRefGoogle Scholar
[MKS]Magnus, W., Karass, A. & Solitar, D.. Combinatorial Group Theory. Dover, 1971.Google Scholar
[M]Milnor, J.. A duality theorem for Reidemeister torsion. Ann. Math. 76 (1962), 137–147.CrossRefGoogle Scholar
[S]Sanov, I. N.. A property of a representation of a free group. Doklady Akad. Nauk SSR 57 (1947), 657–659.Google Scholar
[Tl]Thurston, W. P.. On the geometry and dynamics of diffeomorphisms of surfaces I. Preprint.Google Scholar
[T2]Thurston, W. P.. A norm for the homology of 3-manifolds. Preprint.Google Scholar