Typicality of periodic optimization over an expanding circle map
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912232957280256 |
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| author | Gao, Rui Shen, Weixiao Zhang, Ruiqin |
| author_facet | Gao, Rui Shen, Weixiao Zhang, Ruiqin |
| contents | We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical $C^r$ performance function has a unique maximizing measure and the unique maximizing measure is supported on a periodic orbit, for $r=1,2,\cdots,\infty,ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Typicality of periodic optimization over an expanding circle map Gao, Rui Shen, Weixiao Zhang, Ruiqin Dynamical Systems We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical $C^r$ performance function has a unique maximizing measure and the unique maximizing measure is supported on a periodic orbit, for $r=1,2,\cdots,\infty,ω$. |
| title | Typicality of periodic optimization over an expanding circle map |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.10949 |