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Subshifts on infinite alphabets and their entropy
Sharwin RezagholiAbstract
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:
- 07.07.20
- Published:
- 07.07.20
- MSC Codes:
- 05C50, 05C63, 37B10, 37B40, 68R15
- Keywords:
- Infinite graphs, Symbolic Dynamics, Topological entropy