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MiS Preprint

Subshifts on infinite alphabets and their entropy

Sharwin Rezagholi


We generalize symbolic dynamics to infinite alphabets by endowing the alphabet with the cofinite topology. The topological entropy is shown to be equal to the supremum of the growth rate of the complexity function with respect to finite subalphabets. For the case of topological Markov chains induced by infinite graphs, our approach yields the same entropy as the approach of Gurevich via Alexandrov compactification [B.M. Gurevich, Topological entropy of enumerable Markov chains, 1969, Soviet Mathematics Doklady 10:4, 911-915].

MSC Codes:
05C50, 05C63, 37B10, 37B40, 68R15
Infinite graphs, Symbolic Dynamics, Topological entropy

Related publications

2020 Journal Open Access
Sharwin Rezagholi

Subshifts on infinite alphabets and their entropy

In: Entropy, 22 (2020) 11, p. 1293