Priestley Duality and Representations of Global Dynamics

Abstract 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.