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<p>We study Bowen’s specification property (abbr. BSP) for induced systems on the space of random probability measures arising from skew product dynamics. We prove that if the skew product system satisfies the random BSP, then the induced system on the space of random probability measures with a given marginal measure possesses the BSP. This result can be applied to a broad class of partially hyperbolic systems, and the skew product system generated by random perturbations of topologically mixing Anosov diffeomorphisms.</p>

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Bowen’s Specification Property for Induced Dynamics on Spaces of Random Probability Measures

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Xue Liu,
  • Xiao Ma

摘要

We study Bowen’s specification property (abbr. BSP) for induced systems on the space of random probability measures arising from skew product dynamics. We prove that if the skew product system satisfies the random BSP, then the induced system on the space of random probability measures with a given marginal measure possesses the BSP. This result can be applied to a broad class of partially hyperbolic systems, and the skew product system generated by random perturbations of topologically mixing Anosov diffeomorphisms.