Cusp Excursions on Parameter Spaces
Jayadev S. Athreya
TL;DR
This paper investigates the dynamics of SL(d, R) actions on non-compact spaces, providing elementary proofs of logarithm laws and applications to equidistribution and Diophantine approximation.
Contribution
It offers new elementary proofs of logarithm laws for horocycle flows and extends applications to quantitative equidistribution and Diophantine approximation.
Findings
Elementary proofs of logarithm laws for horocycle flows
Applications to quantitative equidistribution
Advances in Diophantine approximation
Abstract
We prove several results for dynamics of -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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