Geodesic cusp excursions and metric diophantine approximation

Details Geodesic cusp excursions and metric diophantine approximation Geodesic cusp excursions and metric diophantine approximation

2007-09-04

arxiv.org/abs/0709.0313v2

Math. Res. Lett. 16 (2009), no.1, 67--85

Mathematics

Geometric Topology

20 pages, see published paper for final edition

Scientific paper

We derive several results that describe the rate at which a generic geodesic makes excursions into and out of a cusp on a finite area hyperbolic surface and relate them to approximation with respect to the orbit of infinity for an associated Fuchsian group. This provides proofs of some well known theorems from metric diophantine approximation in the context of Fuchsian groups. It also gives new results in the classical setting.

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