Asymptotic h-expansiveness rate of C∞ maps

David Burguet; Gang Liao; Jiagang Yang

doi:10.1112/plms/pdv031

Asymptotic h-expansiveness rate of C^∞ maps

David Burguet
, Gang Liao
, Jiagang Yang

École Polytechnique

School of Mathematical Sciences
Tsinghua University
Departamento de Geometria
Universidade Federal Fluminense

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

9 Citations (Scopus)

Résumé

We study the rate of convergence to zero of the tail entropy of C^∞ maps. We give an upper bound of this rate in terms of the growth in k of the derivative of order k and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to C^r (r ≥ 2) robustly non-h-expansive dynamical systems.

langue originale	Anglais
Pages (de - à)	381-419
Nombre de pages	39
journal	Proceedings of the London Mathematical Society
Volume	111
Numéro de publication	2
Les DOIs	https://doi.org/10.1112/plms/pdv031
état	Publié - 1 janv. 2015

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10.1112/plms/pdv031

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title = "Asymptotic h-expansiveness rate of C∞ maps",

abstract = "We study the rate of convergence to zero of the tail entropy of C∞ maps. We give an upper bound of this rate in terms of the growth in k of the derivative of order k and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to Cr (r ≥ 2) robustly non-h-expansive dynamical systems.",

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AB - We study the rate of convergence to zero of the tail entropy of C∞ maps. We give an upper bound of this rate in terms of the growth in k of the derivative of order k and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to Cr (r ≥ 2) robustly non-h-expansive dynamical systems.

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DO - 10.1112/plms/pdv031

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Asymptotic h-expansiveness rate of C∞ maps

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Asymptotic h-expansiveness rate of C^∞ maps