Examples of minimal diffeomorphisms on $\mathbb {T}^{2}$ semiconjugate to an ergodic translation
Volume 222 / 2013
Fundamenta Mathematicae 222 (2013), 63-97
MSC: Primary 37E30; Secondary 37B05.
DOI: 10.4064/fm222-1-4
Abstract
We prove that for every $\epsilon >0$ there exists a minimal diffeomorphism $f:\mathbb {T}^{2}\rightarrow \mathbb {T}^{2}$ of class $C^{3-\epsilon }$ and semiconjugate to an ergodic translation with the following properties: zero entropy, sensitivity to initial conditions, and Li–Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé's example of a derived-from-Anosov diffeomorphism on $\mathbb {T}^3.$
