Entropy and exact Devaney chaos on totally regular continua

Details Entropy and exact Devaney chaos on totally regular continua Entropy and exact Devaney chaos on totally regular continua

2011-12-27

arxiv.org/abs/1112.6017v2

Mathematics

Dynamical Systems

18 pages; the construction of length-expanding Lipschitz maps was moved into arXiv:1203.2352

Scientific paper

We study topological entropy of exactly Devaney chaotic maps on totally regular continua, i.e. on (topologically) rectifiable curves. After introducing the so-called P-Lipschitz maps (where P is a finite invariant set) we give an upper bound for their topological entropy. We prove that if a non-degenerate totally regular continuum X contains a free arc which does not disconnect X or if X contains arbitrarily large generalized stars then X admits an exactly Devaney chaotic map with arbitrarily small entropy. A possible application for further study of the best lower bounds of topological entropies of transitive/Devaney chaotic maps is indicated.

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