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Uspekhi Mat. Nauk, 1996, Volume 51, Issue 5(311), Pages 3–42 (Mi umn1012)  

This article is cited in 76 scientific papers (total in 76 papers)

Planar structures and billiards in rational polygons: the Veech alternative

Ya. B. Vorobets

M. V. Lomonosov Moscow State University

DOI: https://doi.org/10.4213/rm1012

Full text: PDF file (552 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1996, 51:5, 779–817

Bibliographic databases:

UDC: 517.938
MSC: 52C30
Received: 25.06.1996

Citation: Ya. B. Vorobets, “Planar structures and billiards in rational polygons: the Veech alternative”, Uspekhi Mat. Nauk, 51:5(311) (1996), 3–42; Russian Math. Surveys, 51:5 (1996), 779–817

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. 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
    2. O. N. Ageev, “Dynamical systems with arbitrary spectrum multiplicity function”, Russian Math. Surveys, 53:5 (1998), 1079–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Pierre Arnoux, Pascal Hubert, “Fractions continues sur les surfaces de Veech”, J Anal Math, 81:1 (2000), 35  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Hubert, P, “Veech groups and polygonal coverings”, Journal of Geometry and Physics, 35:1 (2000), 75  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Gutkin, E, “Affine mappings of translation surfaces: Geometry and arithmetic”, Duke Mathematical Journal, 103:2 (2000), 191  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Kenyon, R, “Billiards on rational-angled triangles”, Commentarii Mathematici Helvetici, 75:1 (2000), 65  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Kholodenko, AL, “Use of quadratic differentials for description of defects and textures in liquid crystals and 2+1 gravity”, Journal of Geometry and Physics, 33:1–2 (2000), 59  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Gutkin E., “Branched coverings and closed geodesics in flat surfaces, with applications to billiards”, Dynamical Systems: From Crystal To Chaos, 2000, 259–273  crossref  mathscinet  zmath  isi
    9. Bogomolny, E, “Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems”, Communications in Mathematical Physics, 222:2 (2001), 327  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
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    14. McMullen, CT, “Billiards and Teichmüller curves on Hilbert modular surfaces”, Journal of the American Mathematical Society, 16:4 (2003), 857  crossref  mathscinet  zmath  isi  scopus  scopus
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    32. JOHN SMILLIE, BARAK WEISS, “Veech’s dichotomy and the lattice property”, Ergod Th Dynam Sys, 2008, 1  crossref  mathscinet  isi  scopus  scopus
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    40. 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  crossref  mathscinet  zmath  isi
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