Joint typical periodic optimization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911647337021440 |
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| author | Hao, Zelai Huang, Yinying Jenkinson, Oliver Li, Zhiqiang |
| author_facet | Hao, Zelai Huang, Yinying Jenkinson, Oliver Li, Zhiqiang |
| contents | We prove a generalised Yuan--Hunt--Mañé Conjecture: if $\mathcal{F}$ is the Banach space of $α$-Hölder functions, and $\mathcal{T}$ is either a space of Lipschitz expanding maps, or of Anosov diffeomorphisms, or the family of beta-transformations on the interval, there is an open dense subset of $\mathcal{T}\times\mathcal{F}$ consisting of map-function pairs whose maximizing invariant measure is unique and supported on a periodic orbit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_12269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint typical periodic optimization Hao, Zelai Huang, Yinying Jenkinson, Oliver Li, Zhiqiang Dynamical Systems Primary: 37A99, Secondary: 37A05, 37B25, 37B65, 37C20, 37C50, 37D20, 37D35, 37E05, 37A44 We prove a generalised Yuan--Hunt--Mañé Conjecture: if $\mathcal{F}$ is the Banach space of $α$-Hölder functions, and $\mathcal{T}$ is either a space of Lipschitz expanding maps, or of Anosov diffeomorphisms, or the family of beta-transformations on the interval, there is an open dense subset of $\mathcal{T}\times\mathcal{F}$ consisting of map-function pairs whose maximizing invariant measure is unique and supported on a periodic orbit. |
| title | Joint typical periodic optimization |
| topic | Dynamical Systems Primary: 37A99, Secondary: 37A05, 37B25, 37B65, 37C20, 37C50, 37D20, 37D35, 37E05, 37A44 |
| url | https://arxiv.org/abs/2502.12269 |