Symbolic Dynamics and Markov Partitions
动力系统
2016-09-06 v1
摘要
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.
引用
@article{arxiv.math/9607214,
title = {Symbolic Dynamics and Markov Partitions},
author = {Roy Adler},
journal= {arXiv preprint arXiv:math/9607214},
year = {2016}
}