A Devaney-chaotic map with positive entropy on a symbolic space

Abstract

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let A = [0, 1, . . ., p -1]. We define a continuous map on AZ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points. 2019 Korean Mathematical Society.