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<p>In this manuscript, we consider a non-autonomous dynamical system. Using the Carathéodory structure, we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian [24]. Moreover, we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems. Finally, we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.</p>

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The variational principle for a BS dimension of subsets for non-autonomous dynamical systems

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Zhongxuan Yang,
  • Xiaojun Huang

摘要

In this manuscript, we consider a non-autonomous dynamical system. Using the Carathéodory structure, we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian [24]. Moreover, we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems. Finally, we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.