On mostly expanding diffeomorphisms

Martin Andersson; Carlos H. Vásquez

doi:10.1017/etds.2017.17

On mostly expanding diffeomorphisms

Martin Andersson, Carlos H. Vásquez

INSTITUTE OF MATHEMATICS

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11 Scopus citations

Abstract

In this work, we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such a class is -open, r > 1, among the partially hyperbolic diffeomorphisms and we prove that the mostly expanding condition guarantees the existence of physical measures and provides more information about the statistics of the system. Mañé's classical derived-from-Anosov diffeomorphism on belongs to this set.

Original language	English
Pages (from-to)	2838-2859
Number of pages	22
Journal	Ergodic Theory and Dynamical Systems
Volume	38
Issue number	8
DOIs	https://doi.org/10.1017/etds.2017.17
State	Published - 1 Dec 2018

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abstract = "In this work, we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such a class is -open, r > 1, among the partially hyperbolic diffeomorphisms and we prove that the mostly expanding condition guarantees the existence of physical measures and provides more information about the statistics of the system. Ma{\~n}{\'e}'s classical derived-from-Anosov diffeomorphism on belongs to this set.",

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N2 - In this work, we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such a class is -open, r > 1, among the partially hyperbolic diffeomorphisms and we prove that the mostly expanding condition guarantees the existence of physical measures and provides more information about the statistics of the system. Mañé's classical derived-from-Anosov diffeomorphism on belongs to this set.

AB - In this work, we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such a class is -open, r > 1, among the partially hyperbolic diffeomorphisms and we prove that the mostly expanding condition guarantees the existence of physical measures and provides more information about the statistics of the system. Mañé's classical derived-from-Anosov diffeomorphism on belongs to this set.

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JO - Ergodic Theory and Dynamical Systems

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On mostly expanding diffeomorphisms

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