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

Abstract

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 and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé's example of derived from Anosov diffeomorphism on $\T^3.$

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