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The probabilistic approach to chaotic systems is illustrated, starting from the definition of invariant density. The properties of ergodicity and mixing are discussed, as well as the interpretation in terms of Markov chains. Finally, the role of the ergodic hypothesis in the context of statistical mechanics is discussed in details.

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Probability and Deterministic Chaotic Systems

  • 章节

  • 发表日期：

    2026年

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  • Guido Boffetta,
  • Angelo Vulpiani

摘要

The probabilistic approach to chaotic systems is illustrated, starting from the definition of invariant density. The properties of ergodicity and mixing are discussed, as well as the interpretation in terms of Markov chains. Finally, the role of the ergodic hypothesis in the context of statistical mechanics is discussed in details.