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u-entropy

Ergodic Theory and Dynamical Systems (1)

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Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov
Part of
- Dynamical systems with hyperbolic behavior
- Ergodic theory
RAUL URES, MARCELO VIANA, FAN YANG, JIAGANG YANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 1 / January 2024

Published online by Cambridge University Press:

27 February 2023, pp. 290-333

Print publication:

January 2024
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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.