Cusp Excursions on Parameter Spaces

Details Cusp Excursions on Parameter Spaces Cusp Excursions on Parameter Spaces

2011-04-14

arxiv.org/abs/1104.2797v2

Mathematics

Dynamical Systems

27 pages, edited and re-submitted to London Math Society. Changes are minor, mainly in exposition

Scientific paper

We prove several results for dynamics of $SL(d, \R)$-actions on non-compact
parameter spaces by studying associated discrete sets in Euclidean spaces. This
allows us to give elementary proofs of logarithm laws for horocycle flows on
hyperbolic surfaces and moduli spaces of flat surfaces. We also give
applications to quantitative equidistribution and Diophantine approximation.

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