On the almost sure spiraling of geodesics in negatively curved manifolds

Sa’ar Hersonsky, Frédéric Paulin

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish
Pages (from-to)271-314
Number of pages44
JournalJournal of Differential Geometry
Issue number2
StatePublished - 1 Jan 2010
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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