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TMF, 2001, Volume 127, Number 1, Pages 110–124 (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

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.

DOI: https://doi.org/10.4213/tmf451

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

Bibliographic databases:

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

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. S. V. Naydenov, V. V. Yanovskii, “Geometric-Dynamic Approach to Billiard Systems: II. Geometric Features of Involutions”, Theoret. and Math. Phys., 129:1 (2001), 1408–1420  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. V. Naydenov, V. V. Yanovskii, “Invariant Distributions in Systems with Elastic Reflections”, Theoret. and Math. Phys., 130:2 (2002), 256–270  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Naydenov, SV, “Problem of a billiard in symmetric coordinates”, JETP Letters, 75:8 (2002), 426  mathnet  mathnet  crossref  adsnasa  isi  scopus  scopus
    4. Baryakhtar, VG, “Chaos in composite billiards”, Journal of Experimental and Theoretical Physics, 103:2 (2006), 292  crossref  adsnasa  isi  scopus  scopus
    5. Bolotin, YL, “The world of chaos”, Problems of Atomic Science and Technology, 2007, no. 3, 255  isi
    6. Naydenov, SV, “Polymorphous billiard as a new type of billiards with chaotic ray dynamics”, Problems of Atomic Science and Technology, 2007, no. 3, 285  isi
    7. D. M. Naplekov, V. P. Seminozhenko, V. V. Yanovskii, “Uravnenie sostoyaniya idealnogo gaza v soobschayuschikhsya sosudakh”, Nelineinaya dinam., 9:3 (2013), 435–457  mathnet
    8. S. V. Naydenov, D. M. Naplekov, V. V. Yanovskii, “New mechanism of chaos in triangular billiards”, JETP Letters, 98:8 (2013), 496–502  mathnet  crossref  crossref  isi  elib
    9. Naplekov D.M., Semynozhenko V.P., Yanovsky V.V., “Equation of State of An Ideal Gas With Nonergodic Behavior in Two Connected Vessels”, Phys. Rev. E, 89:1 (2014), 012920  crossref  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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