Priestley duality and representations of recurrent dynamics

For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global dynamics. In the classical setting, the chain recurrent set, int...

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Bibliographic Details
Main Authors Kalies, William, Vandervorst, Robert
Format Journal Article
LanguageEnglish
Published 19.07.2024
Subjects
Mathematics - Dynamical Systems
Mathematics - General Topology
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Summary:For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global dynamics. In the classical setting, the chain recurrent set, introduced by C. Conley, is an example of an ordered Stone space or Priestley space. 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.
DOI:10.48550/arxiv.2407.14359