Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/12269
Título: | Finite resolution dynamics |
Autor(es): | Luzzatto, Stefano Pilarczyk, Pawel |
Palavras-chave: | Dynamical system Finite resolution Open cover Combinatorial dynamics Rigorous numerics Directed graph Transitivity Mixing Algorithm |
Data: | Abr-2011 |
Editora: | Springer |
Revista: | Foundations of Computational Mathematics |
Citação: | "Foundations of Computational Mathematics." ISSN 1615-3375. 11:2 (Abr. 2011) 211-239. |
Resumo(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 $10^{-5}$. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/12269 |
DOI: | 10.1007/s10208-010-9083-z |
ISSN: | 1615-3375 1615-3383 |
Versão da editora: | http://www.springerlink.com/ |
Arbitragem científica: | yes |
Acesso: | Acesso restrito UMinho |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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FiniteResolutionDynamics.pdf Acesso restrito! | Main article | 468,01 kB | Adobe PDF | Ver/Abrir |