Statistical Properties of Generalized Horseshoe Maps
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911354919583744 |
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| author | Fakhari, Abbas Soufi, Mohammad |
| author_facet | Fakhari, Abbas Soufi, Mohammad |
| contents | We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure. Under the virtually expanding condition, this measure is absolutely continuous with respect to Lebesgue measure, with density in the Sobolev space $H_μ$, for some $μ<1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02003 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Statistical Properties of Generalized Horseshoe Maps Fakhari, Abbas Soufi, Mohammad Dynamical Systems We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure. Under the virtually expanding condition, this measure is absolutely continuous with respect to Lebesgue measure, with density in the Sobolev space $H_μ$, for some $μ<1/2$. |
| title | Statistical Properties of Generalized Horseshoe Maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2601.02003 |