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This is a Quantitative Study study.

October 9, 20250 citationsOpen Access

Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves

JPJorge Luis Crisostomo Parejas RCRichard Cubas

Key Points

Establishing an upper limit on the number of maximal entropy ergodic measures advances understanding of complex dynamical systems.
These measures are identified through analysis of topologically transitive partially hyperbolic diffeomorphisms and compact center leaves.
Comprehensive characterization of these measures enhances foundational knowledge in ergodic theory and dynamical systems.
Revealing the nature of ergodic measures supports future studies in the context of dynamical systems with varying stability.

Abstract

In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on T³. Furthermore, we establish a comprehensive characterization of the support of these measures.

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Parejas et al. (2025) studied this question.

synapsesocial.com/papers/68e7f0af2d7e30942762c987 https://doi.org/10.48550/arxiv.2507.23081

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October 9, 20250 citationsOpen Access

Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves

View Full Paper

JPJorge Luis Crisostomo Parejas RCRichard Cubas

Key Points

Establishing an upper limit on the number of maximal entropy ergodic measures advances understanding of complex dynamical systems.
These measures are identified through analysis of topologically transitive partially hyperbolic diffeomorphisms and compact center leaves.
Comprehensive characterization of these measures enhances foundational knowledge in ergodic theory and dynamical systems.
Revealing the nature of ergodic measures supports future studies in the context of dynamical systems with varying stability.

Abstract

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Cite This Study

Parejas et al. (2025) studied this question.

synapsesocial.com/papers/68e7f0af2d7e30942762c987 https://doi.org/10.48550/arxiv.2507.23081

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