Typical Uniqueness in Ergodic Optimization
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910980271767552 |
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| author | Jenkinson, Oliver Li, Xiaoran Liao, Yuexin Zhang, Yiwei |
| author_facet | Jenkinson, Oliver Li, Xiaoran Liao, Yuexin Zhang, Yiwei |
| contents | For ergodic optimization on any topological dynamical system, with real-valued potential function $f$ belonging to any separable Banach space $B$ of continuous functions, we show that the $f$-maximizing measure is typically unique, in the strong sense that a countable collection of hypersurfaces contains the exceptional set of those $f\in B$ with non-unique maximizing measure. This strengthens previous results asserting that the uniqueness set is both residual and prevalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Typical Uniqueness in Ergodic Optimization Jenkinson, Oliver Li, Xiaoran Liao, Yuexin Zhang, Yiwei Dynamical Systems For ergodic optimization on any topological dynamical system, with real-valued potential function $f$ belonging to any separable Banach space $B$ of continuous functions, we show that the $f$-maximizing measure is typically unique, in the strong sense that a countable collection of hypersurfaces contains the exceptional set of those $f\in B$ with non-unique maximizing measure. This strengthens previous results asserting that the uniqueness set is both residual and prevalent. |
| title | Typical Uniqueness in Ergodic Optimization |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2506.01518 |