Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-29T02:30:35.695Z Has data issue: false hasContentIssue false
  • English
  • Français

Entropy and semi-conjugacy in dimension two

Published online by Cambridge University Press:  19 September 2008

Michael Handel
Michael Handel
Affiliation:
Department of Mathematics and Computer Science, Lehman College, Bronx, New York 10468, 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 prove that if a diffeomorphism f of a closed surface is homotopic to and has the same topological entropy as a pseudo-Anosov homeomorphism g, then f is semi-conjugate to g. As part of the proof, a necessary and sufficient condition is given for a pseudo-orbit of a pseudo-Anosov homeomorphism g to be shadowed by an actual orbit of g.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 4 , December 1988 , pp. 585 - 596
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

[F1]Fathi, A.. Homotopical stability of pseudo-Anosov maps. Preprint.Google Scholar
[F2]Fathi, A.. An orbit closing proof of Brouwer's lemma on translation arcs. Preprint.Google Scholar
[F-L-P]Fathi, A., Laudenbach, F. & Poenaru, V.. Travaux de Thurston sur les surfaces. Asterisque 66–67 (1979).Google Scholar
[Fr]Franks, J.. Anosov diffeomorphisms. Proceedings of the Symposium in Pure Mathematics 14 (1968) 61–94.CrossRefGoogle Scholar
[H]Handel, M.. Global shadowing of pseudo-Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 5 (1985), 373–377.CrossRefGoogle Scholar
[H-T]Handel, M. & Thurston, W.. New proofs of some results of Nielsen. Adv. Math. 56 (1985), 173–191.CrossRefGoogle Scholar
[M]Miller, R. T.. Nielsen's viewpoint on geodesic laminations. Adv. in Math. 45 (1982), 189–212.CrossRefGoogle Scholar
[T]Thurston, W.. On the geometry and dynamics of diffeomorphisms of surfaces. Preprint.Google Scholar