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<p>In this paper, we establish a dichotomy for ergodic measures of maximal entropy of partially hyperbolic diffeomorphisms with compact one-dimensional center leaves that are virtually skew products over a transitive Anosov homeomorphism. We prove that if the whole manifold is the unique minimal invariant set saturated by the unstable foliation, then exactly one of the following holds: either there exists a unique non-hyperbolic measure of maximal entropy, or there exist exactly two ergodic measures of maximal entropy, both hyperbolic, with center Lyapunov exponents of opposite signs.</p>

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Maximal Entropy Measures for Non-accessible Topological Skew Products

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Richard Javier Cubas Becerra,
  • Ali Tahzibi

摘要

In this paper, we establish a dichotomy for ergodic measures of maximal entropy of partially hyperbolic diffeomorphisms with compact one-dimensional center leaves that are virtually skew products over a transitive Anosov homeomorphism. We prove that if the whole manifold is the unique minimal invariant set saturated by the unstable foliation, then exactly one of the following holds: either there exists a unique non-hyperbolic measure of maximal entropy, or there exist exactly two ergodic measures of maximal entropy, both hyperbolic, with center Lyapunov exponents of opposite signs.