Convergence of the Birkhoff spectrum for nonintegrable observables
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915360083542016 |
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| author | Iommi, Godofredo Todd, Mike Zhao, Boyuan |
| author_facet | Iommi, Godofredo Todd, Mike Zhao, Boyuan |
| contents | We consider interval maps with countably many full branches and observables with polynomial tails. We show that the Birkhoff spectrum is real analytic and that its convergence to the Hausdorff dimension of the repeller is governed by the polynomial tail exponent. This result extends previous work by Arima on more regular observables and demonstrates how the tail behaviour influences the structure of the Birkhoff spectrum. Our proof relies on techniques from thermodynamic formalism and tail estimates for the observable and our applications are to natural observations on Gauss maps, Lüroth transformations as well as to a the first return time for a class of induced Manneville-Pomeau maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of the Birkhoff spectrum for nonintegrable observables Iommi, Godofredo Todd, Mike Zhao, Boyuan Dynamical Systems 37C45, 37D35, 37E05 We consider interval maps with countably many full branches and observables with polynomial tails. We show that the Birkhoff spectrum is real analytic and that its convergence to the Hausdorff dimension of the repeller is governed by the polynomial tail exponent. This result extends previous work by Arima on more regular observables and demonstrates how the tail behaviour influences the structure of the Birkhoff spectrum. Our proof relies on techniques from thermodynamic formalism and tail estimates for the observable and our applications are to natural observations on Gauss maps, Lüroth transformations as well as to a the first return time for a class of induced Manneville-Pomeau maps. |
| title | Convergence of the Birkhoff spectrum for nonintegrable observables |
| topic | Dynamical Systems 37C45, 37D35, 37E05 |
| url | https://arxiv.org/abs/2506.21390 |