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Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

  • ANDREY GOGOLEV (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385709000169
  • Published online: 01 June 2009
Abstract
Abstract

We show by means of a counterexample that a C1+Lip diffeomorphism Hölder conjugate to an Anosov diffeomorphism is not necessarily Anosov. Also we include a result from the 2006 PhD thesis of Fisher: a C1+Lip diffeomorphism Hölder conjugate to an Anosov diffeomorphism is Anosov itself provided that Hölder exponents of the conjugacy and its inverse are sufficiently large.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]Ch. Bonatti , L. Diaz and F. Vuillemin . Topologically transverse nonhyperbolic diffeomorphisms at the boundary of the stable ones. Bol. Soc. Bras. de Mat. 29 (1998), 99144.

[2]M. Carvalho . First homoclinic tangencies in the boundary of Anosov diffeomorphisms. Discrete Continuous Dynam. Syst. A 4 (1998), 765782.

[3]H. Enrich . A heteroclinic bifurction of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 18 (1998), 567608.

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[8]J. Lewowicz . Lyapunov functions and topological stability. J. Differential Equations 38 (1980), 192209.

[9]R. Mañé . Quasi-Anosov diffeomorphisms and hyperbolic manifolds. Trans. Amer. Math. Soc. 229 (1977), 351370.

[11]P. Walters . Anosov diffeomorphisms are topologically stable. Topology 9 (1970), 7178.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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