publication . Preprint . Article . 2009

Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

ANDREY GOGOLEV;
Open Access English
  • Published: 23 Jun 2009
Abstract
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.
Subjects
arXiv: Mathematics::Dynamical SystemsMathematics::Geometric TopologyMathematics::Symplectic Geometry
free text keywords: Mathematics - Dynamical Systems, 37D20, 37D25, Applied Mathematics, General Mathematics, Inverse, Mathematics, Conjugacy class, Pure mathematics, Counterexample, Conjugate, Anosov diffeomorphism, Diffeomorphism, Mathematical analysis
Related Organizations

[BDV98] Ch. Bonatti, L. Diaz, F. Vuillemin. Topologically transverse nonhyperbolic diffeomorphisms at the boundary of the stable ones. Bol. Soc. Bras. de Mat. 29 (1998) 99-144.

[C98] M. Carvalho. First homoclinic tangencies in the boundary of Anosov diffeomorphisms. DCDS-A 4 (1998), 765-782.

[E98] H. Enrich. A heteroclinic bifurction of Anosov diffeomorphisms. Ergodic Theory Dynam. Systems, 18 (1998), 567-608.

[F06] T. Fisher. Ph.D. Thesis. Available online at http://www.etda.libraries.psu.edu/theses/approved/WorldWideFiles/ETD-1174/fisher-thesis-draft.pdf. PennState, (2006).

[K79] A. Katok, Bernoulli diffeomorphisms on surfaces. Ann. of Math. (2) 110 (1979), no. 3, 529-547. [OpenAIRE]

[KH95] A. Katok, B. Hasselblatt. Introduction to the modern theory of dynamical systems. Cambridge University Press, (1995). [OpenAIRE]

[KN08] A. Katok, V. Nitica. Differentiable rigidity of higher rank abelian group actions. In preparation, (2008).

[L80] J. Lewowicz. Lyapunov functions and topological stability. J. Diff. Eq. 38 (1980), 192- 209. [OpenAIRE]

[M77] R. Man˜´e. Quasi-Anosov diffeomorphisms and hyperbolic manifolds. Trans. Amer. Math. Soc. 229 (1977), 351-370.

[Math68] J. Mather. Characterization of Anosov diffeomorphisms. Nederl. Akad. Wetensch. Proc. Ser. A 71 = Indag. Math. 30 (1968) 479-483. [OpenAIRE]

[W70] P. Walters. Anosov diffeomorphisms are topologically stable. Topology 9 (1970), 71-78. [OpenAIRE]

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publication . Preprint . Article . 2009

Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

ANDREY GOGOLEV;