Subshifts on Infinite Alphabets and Their Entropy
We analyze 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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1293 |
| Summary: | We analyze 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 countably infinite graphs, our approach yields the same entropy as the approach of Gurevich We give formulae for the entropy of countable topological Markov chains in terms of the spectral radius in <em>l</em><sup>2</sup><inline-formula><math display="inline"><semantics><msup><mi>l</mi><mn>2</mn></msup></semantics></math></inline-formula>. |
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| ISSN: | 1099-4300 |