caa a22 4500 445331674 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10208-010-9083-z doi (NATIONALLICENCE)springer-10.1007/s10208-010-9083-z Finite Resolution Dynamics [Elektronische Daten] [Stefano Luzzatto, Paweł Pilarczyk] 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 Hénon attractor is mixing at all resolutions coarser than10−5. SFoCM, 2011 Dynamical system nationallicence Finite resolution nationallicence Open cover nationallicence Combinatorial dynamics nationallicence Rigorous numerics nationallicence Directed graph nationallicence Transitivity nationallicence Mixing nationallicence Algorithm nationallicence Luzzatto Stefano Mathematics Department, Imperial College, 180 Queen's Gate, SW7 2AZ, London, UK aut Pilarczyk Paweł Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal aut Foundations of Computational Mathematics Springer-Verlag 11/2(2011-04-01), 211-239 1615-3375 11:2<211 2011 11 10208 https://doi.org/10.1007/s10208-010-9083-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-010-9083-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Luzzatto Stefano Mathematics Department, Imperial College, 180 Queen's Gate, SW7 2AZ, London, UK aut NATIONALLICENCE 700 1- Pilarczyk Paweł Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/2(2011-04-01), 211-239 1615-3375 11:2<211 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer