Ultragraph shift spaces and chaos
Dynamical Systems
2019-02-18 v1
Abstract
Motivated by C*-algebra theory, ultragraph edge shift spaces generalize shifts of finite type to the infinite alphabet case. In this paper we study several notions of chaos for ultragraph shift spaces. More specifically, we show that Li-Yorke, Devaney and distributional chaos are equivalent conditions for ultragraph shift spaces, and characterize this condition in terms of a combinatorial property of the underlying ultragraph. Furthermore, we prove that such properties imply the existence of a compact, perfect set which is distributionally scrambled of type 1 in the ultragraph shift space (a result that is not known for a labelled edge shift (with the product topology) of an infinite graph).
Keywords
Cite
@article{arxiv.1902.05784,
title = {Ultragraph shift spaces and chaos},
author = {Daniel Gonçalves and Bruno Brogni Uggioni},
journal= {arXiv preprint arXiv:1902.05784},
year = {2019}
}