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October 9, 2025Open Access

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

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. (Wed,) studied this question.

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

Authors

Jorge Luis Crisostomo Parejas

National University of San Marcos

Richard Cubas

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

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Abstract

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Authors

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