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On the topological directional entropy

✍ Scribed by Hasan Akın

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
522 KB
Volume
225
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper we study the topological directional entropy of Z 2 -actions generated by one-dimensional linear cellular automata and the shift map σ acting on compact metric space Z Z m . We give a formula, which can be efficiently and rightly computed by means of the coefficients of the local rule f , for the topological directional entropy of Z 2 -action generated by the pair (T f [-r,r] , σ ) in the direction θ (θ ∈ [0, π]). We also generalize the results obtained by Akın [H. Akin, The topological entropy of invertible cellular automata, J. Comput. Appl. Math. 213 (2) (2008) 501-508] to the topological entropy of any invertible one-dimensional linear cellular automata.

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