English

Examples of Minimal Diffeomorphisms on $t^{2}$ Semiconjugated to an Ergodic Translation

Dynamical Systems 2012-08-14 v4

Abstract

We prove that for every ϵ>0\epsilon>0 there exists a minimal diffeomorphism f:\T2\T2f:\T^{2}\rightarrow\T^{2} of class C3ϵC^{3-\epsilon} and semiconjugate to an ergodic traslation, and have the following properties: zero entropy, sensitivity with respect to initial conditions and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Ma\~{n}\'e's example of derived from Anosov diffeomorphism on \T3.\T^3.

Keywords

Cite

@article{arxiv.1009.0485,
  title  = {Examples of Minimal Diffeomorphisms on $t^{2}$ Semiconjugated to an Ergodic Translation},
  author = {Alejandro Passeggi and Martin Sambarino},
  journal= {arXiv preprint arXiv:1009.0485},
  year   = {2012}
}