Communications of the
Korean Mathematical Society CKMS

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 Deva\-ney-chaos and pos itive topological entropy seem to be the strongest. Let $A= \{0,1, \ldots, p-1\}$. We define a continuous map on $ A^{\mathbb Z}$ 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.

Keywords: discrete chaotic transitive positively expansive entropy

MSC numbers: Primary 54H20, 37B10