Chaos on compact metric spaces generated from symbolic dynamical systems
Dynamical Systems
2017-10-18 v1
Abstract
We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a decomposition space which is induced by a chaotic map of symbolic dynamics. In particular, the chaotic character of the tent map and the baker map on [0,1] are reconsidered based on decomposition dynamics involving symbolic dynamics with different two chaotic maps. As an example of compact metric space we exhibit a chaotic map existing on any given finite graph.
Keywords
Cite
@article{arxiv.1710.06106,
title = {Chaos on compact metric spaces generated from symbolic dynamical systems},
author = {Shousuke Ohmori},
journal= {arXiv preprint arXiv:1710.06106},
year = {2017}
}