Symbolic Dynamics and Markov Partitions

Details Symbolic Dynamics and Markov Partitions Symbolic Dynamics and Markov Partitions

1996-07-02

arxiv.org/abs/math/9607214v1

Mathematics

Dynamical Systems

Scientific paper

The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a general theory of representing dynamical systems by symbolic systems by means of so-called Markov partitions. We apply the results to one of the more tractable examples: namely hyperbolic automorphisms of the two dimensional torus. While there are some results in higher dimensions, this area remains a fertile one for research.

Affiliated with

Also associated with

No associations

Rating

Symbolic Dynamics and Markov Partitions 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 Symbolic Dynamics and Markov Partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symbolic Dynamics and Markov Partitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-84881