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On equilibrium states for partially hyperbolic horseshoes

Published online by Cambridge University Press:  04 July 2016

I. RIOS  and
J. SIQUEIRA
I. RIOS
Affiliation:
Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Prof. Marcos Waldemar de Freitas Reis, S/N - Bloco H, 4o Andar, 24210-201 Niterǿi, Brazil email rios@mat.uff.br
J. SIQUEIRA
Affiliation:
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal email jaqueline.rocha@fc.up.pt
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Abstract

We prove the existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Hölder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction, of a family of partially hyperbolic horseshoes introduced by Díaz et al [Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes. Ergod. Th. & Dynam. Sys.29 (2009), 433–474]. For the original three-dimensional system we consider potentials with small variation, constant on local stable manifolds, obtaining existence and uniqueness of equilibrium states.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 1 , February 2018 , pp. 301 - 335
Copyright
© Cambridge University Press, 2016 

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