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This article is cited in 9 scientific papers (total 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
Citation:
S. V. Naydenov, V. V. Yanovskii, “Geometric-Dynamic Approach to Billiard Systems: I. Projective Involution of a Billiard, Direct and Inverse Problems”, TMF, 127:1 (2001), 110–124; Theoret. and Math. Phys., 127:1 (2001), 500–512
Linking options:
https://www.mathnet.ru/eng/tmf451https://doi.org/10.4213/tmf451 https://www.mathnet.ru/eng/tmf/v127/i1/p110
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Abstract page: | 538 | Full-text PDF : | 221 | References: | 75 | First page: | 2 |
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