Mathematical Research Letters

Volume 3, Issue 3, May 1996 pp. 391-403.

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

Authors: Eugene Gutkin and Chris Judge
Author institution: University of Southern California, and Indiana University

Summary: 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.

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