Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy

Details Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy

2011-12-06

arxiv.org/abs/1112.1191v1

Mathematics

Dynamical Systems

21 pages

Scientific paper

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.

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