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On the almost sure spiraling of geodesics in negatively curved manifolds

Sa’ar Hersonsky University of Georgia Frédéric Paulin D´epartement de Math´ematique et Applications

Differential Geometry mathscidoc:1609.10184

Journal of Differential Geometry, 85, (2), 271-314, 2010
Given a negatively curved geodesic metric space M, we study the almost sure asymptotic penetration behavior of (locally) geodesic lines of M into small neighborhoods of points, of closed geodesics, and of other compact (locally) convex subsets of M. We prove Khintchine-type and logarithm law-type results for the spiraling of geodesic lines around these objets. As a consequence in the tree setting, we obtain Diophantine approximation results of elements of non-archimedian local fields by quadratic irrational ones.
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@inproceedings{sa’ar2010on,
  title={ON THE ALMOST SURE SPIRALING OF GEODESICS IN NEGATIVELY CURVED MANIFOLDS},
  author={Sa’ar Hersonsky, and Frédéric Paulin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911220039994566841},
  booktitle={Journal of Differential Geometry},
  volume={85},
  number={2},
  pages={271-314},
  year={2010},
}
Sa’ar Hersonsky, and Frédéric Paulin. ON THE ALMOST SURE SPIRALING OF GEODESICS IN NEGATIVELY CURVED MANIFOLDS. 2010. Vol. 85. In Journal of Differential Geometry. pp.271-314. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911220039994566841.
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