Title

Chain Recurrence Rates and Topological Entropy

Authors

David S. Richeson, Dickinson College
Jim Wiseman

Document Type

Article

Publication Date

12-2008

Department

Mathematics

Language

English

Publication Title

Topology and its Applications

Abstract

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (chain recurrence and chain mixing times). We give upper and lower bounds for these recurrence times and relate the chain mixing time to topological entropy.

Comments

Published as:
Richeson, David, and Jim Wiseman. "Chain Recurrence Rates and Topological Entropy." Topology and its Applications 156, no. 2 (2008): 251-261. https://www.sciencedirect.com/science/article/pii/S0166864108002526

© 2008 Elsevier B.V. All rights reserved.

This author post-print is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit Science Direct’s Website.

© 2008. This publication is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/.

DOI

10.1016/j.topol.2008.07.005

Recommended Citation

Richeson, David S. and Wiseman, Jim, "Chain Recurrence Rates and Topological Entropy" (2008). Dickinson College Faculty Publications. Paper 1396.
https://scholar.dickinson.edu/faculty_publications/1396