Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T05:38:27.994Z Has data issue: false hasContentIssue false
  • English
  • Français

An example of a planar Anosov diffeomorphism without fixed points

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  06 December 2019

SHIGENORI MATSUMOTO
SHIGENORI MATSUMOTO*
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda, Surugadai, Chiyoda-ku, Tokyo, 101-8308, Japan email [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct an example of a fixed point free Anosov diffeomorphism of the plane, which is not topologically conjugate to a translation.

Keywords

Anosov diffeomorphismfixed pointfoliation

MSC classification

Primary: 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Secondary: 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 3 , March 2021 , pp. 923 - 934
Check for updates
Copyright
© Cambridge University Press, 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Groisman, J. and Nitecki, Z.. Foliations and conjugacy, II: The Mendes conjecture for time-one maps of flows. Ergod. Th. & Dynam. Sys., to appear. Preprint, arXiv:1812.04689.Google Scholar
Mendes, P.. On Anosov diffeomorphisms on the plane. Proc. Amer. Math. Soc. 63 (1977), 231–235.CrossRefGoogle Scholar
White, W.. An Anosov translation. Proc. Symp. on Dynamical Systems (University of Bahia, Salvador, Brasil, 26 July–14 August 1971). Ed. Peixoto, M. M.. Academic Press, 1973, pp. 667–670.Google Scholar