Diffeomorphisms Holder conjugate to Anosov diffeomorphisms

Preprint English OPEN
Gogolev, Andrey;
(2008)
  • Subject: 37D20, 37D25 | Mathematics - Dynamical Systems
    arxiv: Mathematics::Dynamical Systems | Mathematics::Geometric Topology | Mathematics::Symplectic Geometry

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 ... View more
  • References (11)
    11 references, page 1 of 2

    [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.

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

    [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.

    [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.

  • Metrics
Share - Bookmark