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Equidistribution of divergent geodesics in negative curvature

Dynamical Systems 2025-01-08 v1 Differential Geometry

Abstract

In the unit tangent bundle of noncompact finite volume negatively curved Riemannian manifolds, we prove the equidistribution towards the measure of maximal entropy for the geodesic flow of the Lebesgue measure along the divergent geodesic flow orbits, as their complexity tends to infinity. We prove the analogous result for geometrically finite tree quotients, where the equidistribution takes place in the quotient space of geodesic lines towards the Bowen-Margulis measure.

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Cite

@article{arxiv.2501.03925,
  title  = {Equidistribution of divergent geodesics in negative curvature},
  author = {Jouni Parkkonen and Frédéric Paulin and Rafael Sayous},
  journal= {arXiv preprint arXiv:2501.03925},
  year   = {2025}
}

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27 pages