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

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

2010-09-02

arxiv.org/abs/1009.0485v2

Mathematics

Dynamical Systems

Scientific paper

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

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