A Devaney-chaotic map with positive entropy on a symbolic space
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 967-979
Published online July 31, 2019
Shankar Bangalore Ramesh, Chetana Urva Vasu
Surathkal, 575025; University College
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 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
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