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On mostly expanding diffeomorphisms

Published online by Cambridge University Press:  02 May 2017

MARTIN ANDERSSON  and
CARLOS H. VÁSQUEZ
MARTIN ANDERSSON
Affiliation:
Departamento de Matemática Aplicada, Universidade Federal Fluminense, Rua Mário Santos Braga S/N, 24020-140, Niterói – RJ, Brazil email nilsmartin@id.uff.br
CARLOS H. VÁSQUEZ
Affiliation:
Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile email carlos.vasquez@ucv.cl
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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 $C^{r}$-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 $\mathbb{T}^{3}$ belongs to this set.

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Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 8 , December 2018 , pp. 2838 - 2859
Copyright
© Cambridge University Press, 2017 

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