Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909957516951552 |
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| author | Lima, Yuri Matheus, Carlos Melbourne, Ian |
| author_facet | Lima, Yuri Matheus, Carlos Melbourne, Ian |
| contents | We prove a nonstandard central limit theorem and weak invariance principle, with superdiffusive normalisation $(t\log t)^{1/2}$, for geodesic flows on a class of nonpositively curved surfaces with flat cylinder. We also prove that correlations decay at rate $t^{-1}$. An important ingredient of the proof, which is of independent interest, is an improved results on the regularity of the stable/unstable foliations induced by the Green bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces Lima, Yuri Matheus, Carlos Melbourne, Ian Dynamical Systems Differential Geometry We prove a nonstandard central limit theorem and weak invariance principle, with superdiffusive normalisation $(t\log t)^{1/2}$, for geodesic flows on a class of nonpositively curved surfaces with flat cylinder. We also prove that correlations decay at rate $t^{-1}$. An important ingredient of the proof, which is of independent interest, is an improved results on the regularity of the stable/unstable foliations induced by the Green bundles. |
| title | Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2512.11051 |