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Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov

Part of: Ergodic theory Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  27 February 2023

RAUL URES Open the ORCID record for RAUL URES [Opens in a new window] ,
MARCELO VIANA Open the ORCID record for MARCELO VIANA [Opens in a new window] ,
FAN YANG Open the ORCID record for FAN YANG [Opens in a new window]  and
JIAGANG YANG Open the ORCID record for JIAGANG YANG [Opens in a new window]
RAUL URES
Affiliation:
Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, China SUSTech International Center for Mathematics, Shenzhen, Guangdong, China (e-mail: ures@sustech.edu.cn)
MARCELO VIANA
Affiliation:
IMPA, Est. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil (e-mail: viana@impa.br)
FAN YANG
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI, USA (e-mail: yangfa31@msu.edu)
JIAGANG YANG*
Affiliation:
Departamento de Geometria, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Brazil
*
e-mail: yangjg@impa.br
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Abstract

We construct measures of maximal u-entropy for any partially hyperbolic diffeomorphism that factors over an Anosov torus automorphism and has mostly contracting center direction. The space of such measures has finite dimension, and its extreme points are ergodic measures with pairwise disjoint supports.

Keywords

partially hyperbolic diffeomorphismu-entropymostly contracting center

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification 37D30: Partially hyperbolic systems and dominated splittings 37D35: Thermodynamic formalism, variational principles, equilibrium states

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 1 , January 2024 , pp. 290 - 333
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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