Mathematical Research Letters

Volume 3 (1996)

Number 3

The Geometry and Arithmetic of Translation Surfaces with Applications to Polygonal Billiards

Pages: 391 – 403



Eugene Gutkin (University of Southern California)

Chris Judge (Indiana University)


A translation manifold is a manifold whose transition transformations are translations. There is an important connection between the geometry and arithmetic of translation surfaces and dynamics of polygonal billiards. There are also remarkable relations with automorphic forms. In this note we announce results which further develop these connections.

Published 1 January 1996