Gap distributions and homogeneous dynamics

Abstract

We survey the use of dynamics of $SL(2,\mathbb{R})$-actions to understand gap distributions for various sequences of subsets of $[0,1)$, particularly those arising from special trajectories of various two-dimensional dynamical systems. We state and prove an abstract theorem that gives a unified explanation for some of the examples we present.

arXiv commentto appear in Proceedings of ICM Satellite Conference on Geometry, Topology, and Dynamics in Negative Curvarture

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