Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy
Dynamical Systems
2012-09-25 v1
Abstract
We study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e., an open subset homeomorphic to an open interval). A special attention is paid to relationships between topological transitivity, weak and strong topological mixing, dense periodicity and topological entropy as well as to the topological structure of minimal sets. In particular, a trichotomy for minimal sets and a dichotomy for transitive maps are proved.
Keywords
Cite
@article{arxiv.1112.1191,
title = {Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy},
author = {Matúš Dirbák and Ľubomír Snoha and Vladimír Špitalský},
journal= {arXiv preprint arXiv:1112.1191},
year = {2012}
}
Comments
21 pages