This article is cited in 9 papers

Geometric-Dynamic Approach to Billiard Systems: I. Projective Involution of a Billiard, Direct and Inverse Problems

S. V. Naydenov, V. V. Yanovskii

Institute for Single Crystals, National Academy of Sciences of Ukraine

Abstract: We suggest a geometric-dynamic approach to billiards as a special kind of reversible dynamic system and establish their relation to projective transformations (involutions) in the framework of this approach. We state the direct and inverse problems for billiards and derive equations determining the solutions of these problems in general form. Some simplest billiard involutions are calculated. We establish functional relations between the involution of a billiard, the equation for its boundary, and the field of normals to the boundary. We show how the involution is related to the curvature of the billiard boundary.

Received: 31.07.2000

DOI: 10.4213/tmf451

 English version: Theoretical and Mathematical Physics, 2001, 127:1, 500–512

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