Dense periodic optimization for countable Markov shift via Aubry points
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911432504770560 |
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| author | Garibaldi, Eduardo Gomes, João T A |
| author_facet | Garibaldi, Eduardo Gomes, João T A |
| contents | For transitive Markov subshifts over countable alphabets, this note ensures that a dense subclass of locally Hölder continuous potentials admits at most a single periodic probability as a maximizing measure. We resort to concepts analogous to those introduced by Mather and Mañé in the study of globally minimizing curves in Lagrangian dynamics. In particular, given a summable variation potential, we show the existence of a continuous sub-action in the presence of an Aubry point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dense periodic optimization for countable Markov shift via Aubry points Garibaldi, Eduardo Gomes, João T A Dynamical Systems 28D05, 37A05, 37B10 For transitive Markov subshifts over countable alphabets, this note ensures that a dense subclass of locally Hölder continuous potentials admits at most a single periodic probability as a maximizing measure. We resort to concepts analogous to those introduced by Mather and Mañé in the study of globally minimizing curves in Lagrangian dynamics. In particular, given a summable variation potential, we show the existence of a continuous sub-action in the presence of an Aubry point. |
| title | Dense periodic optimization for countable Markov shift via Aubry points |
| topic | Dynamical Systems 28D05, 37A05, 37B10 |
| url | https://arxiv.org/abs/2410.06464 |