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

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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 C^r (r ≥ 2) robustly non-h-expansive dynamical systems.

Original language	English
Pages (from-to)	381-419
Number of pages	39
Journal	Proceedings of the London Mathematical Society
Volume	111
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdv031
Publication status	Published - 1 Jan 2015

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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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JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

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Asymptotic h-expansiveness rate of C∞ maps

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Asymptotic h-expansiveness rate of C^∞ maps