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TitleFinite resolution dynamics
Author(s)Luzzatto, Stefano
Pilarczyk, Pawel
KeywordsDynamical system
Finite resolution
Open cover
Combinatorial dynamics
Rigorous numerics
Directed graph
Issue dateApr-2011
JournalFoundations of Computational Mathematics
Citation"Foundations of Computational Mathematics." ISSN 1615-3375. 11:2 (Abr. 2011) 211-239.
Abstract(s)We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at all resolutions coarser than a given number. Open covers are used to approximate the topology of the phase space in a finite way, and the dynamical system is represented by means of a combinatorial multivalued map. We formulate notions of transitivity and mixing in the finite resolution setting in a computable and consistent way. Moreover, we formulate equivalent conditions for these properties in terms of graphs, and provide effective algorithms for their verification. As an application we show that the Henon attractor is mixing at all resolutions coarser than $10^{-5}$.
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AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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