Finite resolution dynamics. (arXiv:0910.2319v1 [math.DS])

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.

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Original source : http://arxiv.org/abs/0910.2319...