Geodesic
Geometric-Dynamic Approach to Billiard Systems: I.~Projective Involution of a Billiard, Direct and Inverse Problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 110-124

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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. 
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     author = {S. V. Naydenov and V. V. Yanovskii},
     title = {Geometric-Dynamic {Approach} to {Billiard} {Systems:} {I.~Projective} {Involution} of a {Billiard,} {Direct} and {Inverse} {Problems}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2001},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a7/}
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S. V. Naydenov; V. V. Yanovskii. Geometric-Dynamic Approach to Billiard Systems: I.~Projective Involution of a Billiard, Direct and Inverse Problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 110-124. http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a7/