English

Diffeomorphisms Holder conjugate to Anosov diffeomorphisms

Dynamical Systems 2010-06-25 v2

Abstract

We show by means of a counterexample that a C1+LipC^{1+Lip} diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to C3C^3. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a C1+LipC^{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.

Keywords

Cite

@article{arxiv.0809.0529,
  title  = {Diffeomorphisms Holder conjugate to Anosov diffeomorphisms},
  author = {Andrey Gogolev},
  journal= {arXiv preprint arXiv:0809.0529},
  year   = {2010}
}

Comments

15 pages, 4 figures. Comments are welcome. Minor fixes in the second version

R2 v1 2026-06-21T11:16:18.904Z