On the Hausdorff dimension of geodesics that diverge on average
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909601557905408 |
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| author | Riquelme, Felipe Velozo, Anibal |
| author_facet | Riquelme, Felipe Velozo, Anibal |
| contents | In this article we prove that the Hausdorff dimension of geodesic directions that are recurrent and diverge on average coincides with the entropy at infinity of the geodesic flow for any complete, pinched negatively curved Riemannian manifold. Furthermore, we prove that the entropy of a $σ$-finite, infinite, ergodic and conservative invariant measure is bounded from above by the entropy at infinity of the geodesic flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05894 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Hausdorff dimension of geodesics that diverge on average Riquelme, Felipe Velozo, Anibal Dynamical Systems 37C45, 37D40, 37D35, 28A78, 28D20 In this article we prove that the Hausdorff dimension of geodesic directions that are recurrent and diverge on average coincides with the entropy at infinity of the geodesic flow for any complete, pinched negatively curved Riemannian manifold. Furthermore, we prove that the entropy of a $σ$-finite, infinite, ergodic and conservative invariant measure is bounded from above by the entropy at infinity of the geodesic flow. |
| title | On the Hausdorff dimension of geodesics that diverge on average |
| topic | Dynamical Systems 37C45, 37D40, 37D35, 28A78, 28D20 |
| url | https://arxiv.org/abs/2308.05894 |