publication . Article . Preprint . 2008

Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

Andrey Gogolev;
Open Access
  • Published: 02 Sep 2008 Journal: Ergodic Theory and Dynamical Systems, volume 30, pages 441-456 (issn: 0143-3857, eissn: 1469-4417, Copyright policy)
  • Publisher: Cambridge University Press (CUP)
We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large.
Persistent Identifiers
arXiv: Mathematics::Dynamical SystemsMathematics::Geometric TopologyMathematics::Symplectic Geometry
free text keywords: Applied Mathematics, General Mathematics, Mathematics - Dynamical Systems, 37D20, 37D25, Conjugacy class, Diffeomorphism, Pure mathematics, Anosov diffeomorphism, Inverse, Conjugate, Mathematics, Counterexample

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