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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 matsumo@math.cst.nihon-u.ac.jp
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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
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Copyright
© Cambridge University Press, 2019

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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