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<p>Asymptotic global dynamics is fundamentally an order structure. This relationship is naturally characterized in terms of a Priestley space derived from the attractors of a system, which provides an order-theoretic framework for the study of global dynamics. In the classical setting, the representation of the Priestley space is the chain recurrent set, introduced by C. Conley, [<CitationRef CitationID="CR10">10</CitationRef>]. Priestley duality can be applied in the setting of dynamics on arbitrary topological spaces and yields a notion of Hausdorff compactification of the (chain) recurrent set.</p>

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Priestley Duality and Representations of Global Dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月24日

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  • William Kalies,
  • Robert Vandervorst

摘要

Asymptotic global dynamics is fundamentally an order structure. This relationship is naturally characterized in terms of a Priestley space derived from the attractors of a system, which provides an order-theoretic framework for the study of global dynamics. In the classical setting, the representation of the Priestley space is the chain recurrent set, introduced by C. Conley, [10]. Priestley duality can be applied in the setting of dynamics on arbitrary topological spaces and yields a notion of Hausdorff compactification of the (chain) recurrent set.