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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.18736 |
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| _version_ | 1866913068442714112 |
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| author | Garibaldi, Eduardo Gomes, João T A Sobottka, Marcelo |
| author_facet | Garibaldi, Eduardo Gomes, João T A Sobottka, Marcelo |
| contents | For upper semi-continuous potentials defined on shifts over countable alphabets, this paper ensures sufficient conditions for the existence of a maximizing measure. We resort to the concept of blur shift, introduced by T. Almeida and M. Sobottka as a compactification method for countable alphabet shifts consisting of adding new symbols given by blurred subsets of the alphabet. Our approach extends beyond the Markovian case to encompass more general countable alphabet shifts. In particular, we guarantee a convex characterization and compactness for the set of blur invariant probabilities with respect to the discontinuous shift map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximizing measures for countable alphabet shifts via blur shift spaces Garibaldi, Eduardo Gomes, João T A Sobottka, Marcelo Dynamical Systems 37A05 (Primary), 37B10 (Secondary), 28D05 (Ternary) For upper semi-continuous potentials defined on shifts over countable alphabets, this paper ensures sufficient conditions for the existence of a maximizing measure. We resort to the concept of blur shift, introduced by T. Almeida and M. Sobottka as a compactification method for countable alphabet shifts consisting of adding new symbols given by blurred subsets of the alphabet. Our approach extends beyond the Markovian case to encompass more general countable alphabet shifts. In particular, we guarantee a convex characterization and compactness for the set of blur invariant probabilities with respect to the discontinuous shift map. |
| title | Maximizing measures for countable alphabet shifts via blur shift spaces |
| topic | Dynamical Systems 37A05 (Primary), 37B10 (Secondary), 28D05 (Ternary) |
| url | https://arxiv.org/abs/2507.18736 |