On the Hausdorff dimension of geodesics that diverge on average

Fuente: arXiv
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Autori principali: Riquelme, Felipe, Velozo, Anibal
Natura: Preprint
Pubblicazione: 2023
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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