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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
76/2020

Subshifts on infinite alphabets and their entropy

Sharwin Rezagholi

Abstract

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].

Received:
Jul 7, 2020
Published:
Jul 7, 2020
MSC Codes:
05C50, 05C63, 37B10, 37B40, 68R15
Keywords:
Infinite graphs, Symbolic Dynamics, Topological entropy

Related publications

inJournal
2020 Journal Open Access
Sharwin Rezagholi

Subshifts on infinite alphabets and their entropy

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