Chain recurrence rates and topological entropy
By David Richeson, J. Wiseman. 2008
68 citations recorded by the source corpus.
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 e-chains, and the minimal lengths of these e-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.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5736839f701a6ac399a1a93a91a7ec56cb146cbe
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In Computational Theory and Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- On shadowing: Ordinary and ergodic (2010, background): “By [15], f is chain transitive and satisfy the shadowing property.”
- On almost specification and average shadowing properties (2013, background): “By [29], if f n is chain transitive for every n > 0, then it is chain mixing.”