An algorithmic approach to lattices and order in dynamics

Dinesh Kasti, R.C.A.M. Van der vorst, W.D. Kalies

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Abstract

Recurrent versus gradient-like behavior in global dynamics can be characterized via a surjective lattice homomorphism between certain bounded, distributive lattices, that is, between attracting blocks (or neighborhoods) and attractors. Using this characterization, we build finite, combinatorial models in terms of surjective lattice homomorphisms, which lay a foundation for a computational theory for dynamical systems that focuses on Morse decompositions and index lattices. In particular we present an algorithm that builds a combinatorial model that represents a Morse decomposition for the underlying dynamics. We give computational examples that illustrate the theory for both maps and flows.
Original languageEnglish
Pages (from-to)1617-1649
Number of pages33
JournalSIAM Journal on Applied Dynamical Systems
Volume17
Issue number2
Early online date5 Jun 2018
DOIs
Publication statusPublished - 2018

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