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Uspekhi Mat. Nauk, 1992, Volume 47, Issue 3(285), Pages 9–74 (Mi umn4511)  

This article is cited in 22 scientific papers (total in 22 papers)

Periodic billiard trajectories in polygons: generating mechanisms

Ya. B. Vorobets, G. A. Gal'perin, A. M. Stepin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full text: PDF file (4619 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1992, 47:3, 5–80

Bibliographic databases:

UDC: 517.938+517.987
MSC: 51E12, 52Bxx, 37D50
Received: 24.01.1992

Citation: Ya. B. Vorobets, G. A. Gal'perin, A. M. Stepin, “Periodic billiard trajectories in polygons: generating mechanisms”, Uspekhi Mat. Nauk, 47:3(285) (1992), 9–74; Russian Math. Surveys, 47:3 (1992), 5–80

Citation in format AMSBIB
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\paper Periodic billiard trajectories in polygons: generating mechanisms
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\pages 9--74
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\vol 47
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\pages 5--80
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Barry Cipra, Robert M. Hanson, Amy Kolan, “Periodic trajectories in right-triangle billiards”, Phys Rev E, 52:2 (1995), 2066  crossref  mathscinet  isi
    2. G. Galperin, T. Krüger, S. Troubetzkoy, “Local instability of orbits in polygonal and polyhedral billiards”, Comm Math Phys, 169:3 (1995), 463  crossref  mathscinet  adsnasa  isi
    3. Eugene Gutkin, “Billiards in polygons: Survey of recent results”, J Statist Phys, 83:1-2 (1996), 7  crossref  mathscinet  zmath  isi
    4. Ya. B. Vorobets, “Planar structures and billiards in rational polygons”, Russian Math. Surveys, 51:1 (1996), 177–178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Ya. B. Vorobets, “Billiards in rational polygons: Periodic trajectories, symmetries and $d$-stability”, Math. Notes, 62:1 (1997), 56–63  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Serge Troubetzkoy, Nonlinearity, 12:3 (1999), 513  crossref  mathscinet  zmath  isi
    7. A. Yu. Plakhov, A. M. Stepin, “Scattering in multiparticle and billiard dynamical systems”, Sb. Math., 190:7 (1999), 1005–1033  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. YU. SHAHVERDIAN, A. V. APKARIAN, “ON IRREGULAR BEHAVIOR OF NEURON SPIKE TRAINS”, Fractals, 07:01 (1999), 93  crossref
    9. Lorenz Halbeisen, Norbert Hungerbühler, “On Periodic Billiard Trajectories in Obtuse Triangles”, SIAM Rev, 42:4 (2000), 657  crossref  mathscinet  zmath  isi
    10. S. Troubetzkoy, J. Schmeling, “Inhomogeneous Diophantine approximation and angular recurrence for polygonal billiards”, Sb. Math., 194:2 (2003), 295–309  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Zorich A., “Flat surfaces”, Frontiers in Number Theory, Physics and Geometry I - ON RANDOM MATRICES, ZETA FUNCTIONS, AND DYNAMICAL SYSTEMS, 2006, 439–585  isi
    12. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “K modeli negolonomnogo bilyarda”, Nelineinaya dinam., 6:2 (2010), 373–385  mathnet  elib
    13. Lapidus M.L., Niemeyer R.G., “Towards the Koch Snowflake Fractal Billiard: Computer Experiments and Mathematical Conjectures”, Gems in Experimental Mathematics, Contemporary Mathematics, 517, 2010, 231–263  isi
    14. E. A. Gutkin, “Dinamika billiarda: obzornaya statya s aktsentom na nereshennye zadachi”, Nelineinaya dinam., 7:3 (2011), 489–512  mathnet
    15. Eugene Gutkin, “Billiard dynamics: An updated survey with the emphasis on open problems”, Chaos, 22:2 (2012), 026116  crossref
    16. I. A. Kotelnikov, S. S. Popov, M. Romé, “Photon neutralizer as an example of an open billiard”, Phys. Rev. E, 87:1 (2013)  crossref
    17. Robert G. Niemeyer, Michel L. Lapidus, “Sequences of compatible periodic hybrid orbits of prefractal Koch snowflake billiards”, DCDS-A, 33:8 (2013), 3719  crossref
    18. J.P.. Chen, R.G.. Niemeyer, “Periodic billiard orbits of self-similar Sierpiński carpets”, Journal of Mathematical Analysis and Applications, 2014  crossref
    19. Naeem Alkoumi, Felix Schlenk, “Shortest closed billiard orbits on convex tables”, manuscripta math, 2014  crossref
    20. W.P.atrick Hooper, “The invariant measures of some infinite interval exchange maps”, Geom. Topol, 19:4 (2015), 1895  crossref
    21. Lapidus M.L., Miller R.L., Niemeyer R.G., “Nontrivial paths and periodic orbits of the T -fractal billiard table”, Nonlinearity, 29:7 (2016), 2145–2172  crossref  mathscinet  zmath  isi  scopus
    22. A. N. Kirillov, R. V. Alkin, “Ustoichivost periodicheskikh bilyardnykh traektorii v treugolnike”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:1 (2018), 25–39  mathnet  crossref  elib
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