Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914350247182336 |
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| author | Olivares-Vinales, Jorge Yoo, Semin |
| author_facet | Olivares-Vinales, Jorge Yoo, Semin |
| contents | For a class of Fibonacci-like unimodal maps, the restriction to the $ω$-limit set of the unique turning point defines a minimal Cantor system. We construct these Cantor sets geometrically using a nested sequence of finite covers with a tower structure. From this tower structure, we recover the associated Bratteli-Vershik model determined by the cutting times and obtain an explicit formula for the unique ergodic invariant probability measure supported on the $ω$-limit set. We conclude with applications illustrating the scope of the construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21623 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps Olivares-Vinales, Jorge Yoo, Semin Dynamical Systems 37E05, 37E15, 37E25 For a class of Fibonacci-like unimodal maps, the restriction to the $ω$-limit set of the unique turning point defines a minimal Cantor system. We construct these Cantor sets geometrically using a nested sequence of finite covers with a tower structure. From this tower structure, we recover the associated Bratteli-Vershik model determined by the cutting times and obtain an explicit formula for the unique ergodic invariant probability measure supported on the $ω$-limit set. We conclude with applications illustrating the scope of the construction. |
| title | Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps |
| topic | Dynamical Systems 37E05, 37E15, 37E25 |
| url | https://arxiv.org/abs/2602.21623 |