2008/01/10 by Richeson, David, Wiseman, Jim · 3 citations
#37A25 #37B20 #37B40 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.0801.1635
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 \ep-chains, and the minimal lengths of these \ep-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.