The average length of a trajectory in a certain billiard in a flat two-torus

Abstract

We remove a small disc from the flat two-dimensional torus and consider a point-like particle that starts moving from the center of the disc with linear trajectory. We provide asymptotic estimates for the moments of the first exit time, with respect to the velocity, when the radius of the disc tends to zero.

28 pages, 5 figures

References in corpus (2)

• The Lyapunov exponent in the Sinai billiard in the small scatterer limit
• The statistics of the trajectory in a certain billiard in a flat two-torus

Cited by in corpus (5)

• The statistics of the trajectory in a certain billiard in a flat two-torus
• On the Farey fractions with denominators in arithmetic progression
• Distribution of the linear flow length in a honeycomb in the small-scatterer limit
• The distribution of rationals in residue classes
• A density theorem on even Farey fractions