# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Examples of minimal diffeomorphisms on $\mathbb {T}^{2}$ semiconjugate to an ergodic translation

### Tom 222 / 2013

Fundamenta Mathematicae 222 (2013), 63-97 MSC: Primary 37E30; Secondary 37B05. DOI: 10.4064/fm222-1-4

#### Streszczenie

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 $\mathbb {T}^3.$

#### Autorzy

• Alejandro PasseggiInstitut für Analysis
TU-Dresden
Zellescher Weg 12-14, Room C34
Dresden, Germany
e-mail
• Martín SambarinoCMAT, Facultad de Ciencias