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

Volume 222 / 2013

Alejandro Passeggi, Martín Sambarino 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 $\mathbb {T}^3.$

Authors

  • Alejandro PasseggiInstitut für Analysis
    TU-Dresden
    Zellescher Weg 12-14, Room C34
    Dresden, Germany
    e-mail
  • Martín SambarinoCMAT, Facultad de Ciencias
    Universidad de la República
    Uruguay, Igua 4225 esq. Mataojo
    Montevideo, Uruguay
    e-mail

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