• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.967-979
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• 2019

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 $A=\{0,1,{\dots},p-1\}$. 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.