Examples of minimal diffeomorphisms on $\mathbb {T}^{2}$
semiconjugate to an ergodic translation
Fundamenta Mathematicae, Tome 222 (2013) no. 1, pp. 63-97
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\mathbb {T}^3.$
Keywords:
prove every epsilon there exists minimal diffeomorphism mathbb rightarrow mathbb class epsilon semiconjugate ergodic translation following properties zero entropy sensitivity initial conditions yorke chaos these examples obtained through holonomy unstable foliation example derived from anosov diffeomorphism mathbb
Affiliations des auteurs :
Alejandro Passeggi 1 ; Martín Sambarino 2
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title = {Examples of minimal diffeomorphisms on $\mathbb {T}^{2}$
semiconjugate to an ergodic translation},
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semiconjugate to an ergodic translation
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semiconjugate to an ergodic translation
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Alejandro Passeggi; Martín Sambarino. Examples of minimal diffeomorphisms on $\mathbb {T}^{2}$
semiconjugate to an ergodic translation. Fundamenta Mathematicae, Tome 222 (2013) no. 1, pp. 63-97. doi: 10.4064/fm222-1-4
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