Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation

Alejandro Passeggi; Martín Sambarino

Fundamenta Mathematicae, Tome 220 (2013), p. 63-97 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that for every ϵ > 0 there exists a minimal diffeomorphism f: ² → ² of class $C^{3 - ϵ}$ 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 ³.

Publié le : 2013-01-01

Zbl 1321.37043

EUDML-ID : urn:eudml:doc:282748

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     author = {Alejandro Passeggi and Mart\'\i n Sambarino},
     title = {Examples of minimal diffeomorphisms on T2 semiconjugate to an ergodic translation},
     journal = {Fundamenta Mathematicae},
     volume = {220},
     year = {2013},
     pages = {63-97},
     zbl = {1321.37043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-1-4}
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Alejandro Passeggi; Martín Sambarino. Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation. Fundamenta Mathematicae, Tome 220 (2013) pp. 63-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-1-4/