Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation

Alejandro Passeggi, and Martín Sambarino. "Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation." Fundamenta Mathematicae 222.1 (2013): 63-97. <http://eudml.org/doc/282748>.

@article{AlejandroPasseggi2013,
abstract = {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.},
author = {Alejandro Passeggi, Martín Sambarino},
journal = {Fundamenta Mathematicae},
keywords = {Denjoy maps; ergodic translation; minimal homeomorphisms; Mañé’s derived-from-Anosov diffeomorphism; Li-Yorke chaos},
language = {eng},
number = {1},
pages = {63-97},
title = {Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation},
url = {http://eudml.org/doc/282748},
volume = {222},
year = {2013},
}

TY - JOUR
AU - Alejandro Passeggi
AU - Martín Sambarino
TI - Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 1
SP - 63
EP - 97
AB - 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.
LA - eng
KW - Denjoy maps; ergodic translation; minimal homeomorphisms; Mañé’s derived-from-Anosov diffeomorphism; Li-Yorke chaos
UR - http://eudml.org/doc/282748
ER -