2011/12/27 by Špitalský, Vladimír
#37B05 #37B20 #37B40 (Primary) 54H20 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1112.6017
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.