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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 127, Number 1, Pages 110–124
DOI: https://doi.org/10.4213/tmf451 (Mi tmf451) 		 
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
Full-text PDF (250 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf451
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
English version:
Theoretical and Mathematical Physics, 2001, Volume 127, Issue 1, Pages 500–512
DOI: https://doi.org/10.1023/A:1010316025791
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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    This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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