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<p>In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs <i>u</i>-states are hyperbolic. First, we prove the finiteness of ergodic physical measures. By building a criterion, we then obtain the basin covering property for ergodic physical measures under some restriction on the sign of Lyapunov exponents with respect to empirical measures.</p>

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Physical measures on partially hyperbolic diffeomorphisms with multi 1-D centers

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Zeya Mi,
  • Yongluo Cao

摘要

In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs u-states are hyperbolic. First, we prove the finiteness of ergodic physical measures. By building a criterion, we then obtain the basin covering property for ergodic physical measures under some restriction on the sign of Lyapunov exponents with respect to empirical measures.