Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Spatzier, Ralf 2016. On the work of Rodriguez Hertz on rigidity in dynamics. Journal of Modern Dynamics, Vol. 10, Issue. 02, p. 191.

    TIKHOMIROV, SERGEY 2015. Hölder shadowing on finite intervals. Ergodic Theory and Dynamical Systems, Vol. 35, Issue. 06, p. 2000.

    Rodriguez Hertz, Federico and Wang, Zhiren 2014. Global rigidity of higher rank abelian Anosov algebraic actions. Inventiones mathematicae, Vol. 198, Issue. 1, p. 165.

    Bessa, Mário Rocha, Jorge and Torres, Maria Joana 2013. Shades of hyperbolicity for Hamiltonians. Nonlinearity, Vol. 26, Issue. 10, p. 2851.

    Sadovskaya, Victoria 2012. Cohomology of $GL(2,\mathbb{R})$-valued cocycles over hyperbolic systems. Discrete and Continuous Dynamical Systems, Vol. 33, Issue. 5, p. 2085.


Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

  • DOI:
  • Published online: 01 June 2009

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.

Linked references
Hide All

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.

[5]A. Katok . Bernoulli diffeomorphisms on surfaces. Ann. of Math. (2) 110(3) (1979), 529547.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *