On the almost sure spiraling of geodesics in negatively curved manifolds

Details On the almost sure spiraling of geodesics in negatively curved manifolds On the almost sure spiraling of geodesics in negatively curved manifolds

2007-08-24

arxiv.org/abs/0708.3389v2

Journal Of Differential Geometry, Vol85, June 2010 271--315

Mathematics

Differential Geometry

35 pages, 5 figures

Scientific paper

Given a negatively curved geodesic metric space $M$, we study the statistical asymptotic penetration behavior of (locally) geodesic lines of $M$ in small neighborhoods of points, of closed geodesics, and of other compact (locally) convex subsets of $M$. We prove Khintchine-type and logarithme 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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