Priestley duality and representations of recurrent dynamics

2024/07/19 by William D. Kalies, Kalies, William, Robert Vandervorst +1
Arts and Humanities · #06-XX #06D50 #06Dxx #37B20 #37B30 #37Bxx #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Philosophy and History of Science

paper · pdf · doi:10.48550/arxiv.2407.14359

openalex publication_date 2024/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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