Finite Resolution Dynamics

Details Finite Resolution Dynamics Finite Resolution Dynamics

2009-10-13

arxiv.org/abs/0910.2319v3

Mathematics

Dynamical Systems

25 pages. Final version. To appear in Foundations of Computational Mathematics

Scientific paper

10.1007/s10208-010-9083-z

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.

Affiliated with

Also associated with

No associations

Rating

Finite Resolution Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite Resolution Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite Resolution Dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-640359