Open Access
June 2010 On the almost sure spiraling of geodesics in negatively curved manifolds
Sa’ar Hersonsky, Frédéric Paulin
J. Differential Geom. 85(2): 271-314 (June 2010). DOI: 10.4310/jdg/1287580966


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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Sa’ar Hersonsky. Frédéric Paulin. "On the almost sure spiraling of geodesics in negatively curved manifolds." J. Differential Geom. 85 (2) 271 - 314, June 2010.


Published: June 2010
First available in Project Euclid: 20 October 2010

zbMATH: 1229.53050
MathSciNet: MR2732978
Digital Object Identifier: 10.4310/jdg/1287580966

Rights: Copyright © 2010 Lehigh University

Vol.85 • No. 2 • June 2010
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