Finite resolution dynamics Export

@article{citeulike:5938303, abstract = {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 finite resolution. 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 translate notions of transitivity and mixing known for general dynamical systems into the finite setting in a 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 topologically mixing at all resolutions coarser than 10^-5.}, archivePrefix = {arXiv}, author = {Luzzatto, Stefano and Pilarczyk, Pawel}, citeulike-article-id = {5938303}, citeulike-linkout-0 = {http://arxiv.org/abs/0910.2319}, citeulike-linkout-1 = {http://arxiv.org/pdf/0910.2319}, day = {13}, eprint = {0910.2319}, keywords = {discrete, dynamical-system}, month = {Oct}, posted-at = {2009-11-06 15:46:02}, priority = {2}, title = {Finite resolution dynamics}, url = {http://arxiv.org/abs/0910.2319}, year = {2009} }

TY - JOUR ID - citeulike:5938303 L3 - citeulike-article-id:5938303 N2 - 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 finite resolution. 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 translate notions of transitivity and mixing known for general dynamical systems into the finite setting in a 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 topologically mixing at all resolutions coarser than 10^-5. TI - Finite resolution dynamics KW - discrete KW - dynamical-system AU - Luzzatto, Stefano AU - Pilarczyk, Pawel PY - 2009/Oct/13/ UR - http://arxiv.org/abs/0910.2319 ER -