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/

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.