Ya. B. Vorobets, “Ergodicity of billiards in polygons”, Sb. Math., 188:3 (1997), 389

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Sbornik: Mathematics, 1997, Volume 188, Issue 3, Pages 389–434
DOI: https://doi.org/10.1070/sm1997v188n03ABEH000211 (Mi sm211)

This article is cited in 25 scientific papers (total in 25 papers)

Ergodicity of billiards in polygons

Ya. B. Vorobets

M. V. Lomonosov Moscow State University

English version PDF (443 kB) Citations (25) Russian version article

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DOI: https://doi.org/10.1070/sm1997v188n03ABEH000211

Abstract: In the space of all polygons, a topologically massive subset consisting of polygons with ergodic billiard flows is explicitly described. The elements of this set have a specified order of approximation by rational polygons. As intermediate results, constructive versions of the ergodic theorem for the billiard in a rational polygon and for the geodesic flow on a surface with flat structure, and also a constructive quadratic estimate for the growth of the number of saddle connections (singular trajectories) in a flat structure, are proved.

Received: 20.06.1996

Bibliographic databases:

UDC: 517.987.5

MSC: 58F11, 58F17

Language: English

Original paper language: Russian

Citation: Ya. B. Vorobets, “Ergodicity of billiards in polygons”, Sb. Math., 188:3 (1997), 389–434

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm211

https://doi.org/10.1070/sm1997v188n03ABEH000211

https://www.mathnet.ru/eng/sm/v188/i3/p65

This publication is cited in the following 25 articles:

Giovanni Forni, Lecture Notes in Mathematics, 2347, Modern Aspects of Dynamical Systems, 2024, 161
Jordan Orchard, Federico Frascoli, Lamberto Rondoni, Carlos Mejía-Monasterio, “Particle transport in open polygonal billiards: A scattering map”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:12 (2024)
Jozef Bobok, Jernej Činč, Piotr Oprocha, Serge Troubetzkoy, “Periodic points and shadowing for generic Lebesgue measure-preserving interval maps”, Nonlinearity, 35:5 (2022), 2535
Emilio N. M. Cirillo, Matteo Colangeli, Antonio Di Francesco, Martin Kröger, Lamberto Rondoni, “Transport and nonequilibrium phase transitions in polygonal urn models”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32:9 (2022)
Berk P., Fraczek K., de la Rue T., “On Typicality of Translation Flows Which Are Disjoint With Their Inverse”, J. Inst. Math. Jussieu, 19:5 (2020), PII S1474748018000531, 1677–1737
Chen D., Moeller M., Sauvaget A., Zagier D., “Masur-Veech Volumes and Intersection Theory on Moduli Spaces of Abelian Differentials”, Invent. Math., 222:1 (2020), 283–373
Pardo A., “Counting Problem on Wind-Tree Models”, Geom. Topol., 22:3 (2018), 1483–1536
Chen D., Moeller M., Zagier D., “Quasimodularity and Large Genus Limits of Siegel-Veech Constants”, J. Am. Math. Soc., 31:4 (2018), 1059–1163
Huang J., Zhao H., “Ultraslow diffusion and weak ergodicity breaking in right triangular billiards”, Phys. Rev. E, 95:3 (2017), 8–14
Kamaludin Dingle, Jeroen S W Lamb, Joan-Andreu Lázaro-Camí, “Knudsen's law and random billiards in irrational triangles”, Nonlinearity, 26:2 (2013), 369
Dmitri Scheglov, “Growth of periodic orbits and generalized diagonals for typical triangular billiards”, JMD, 7:1 (2013), 31
JEAN-PIERRE CONZE, EUGENE GUTKIN, “On recurrence and ergodicity for geodesic flows on non-compact periodic polygonal surfaces”, Ergod. Th. Dynam. Sys, 2012, 1
Gutkin E., “Billiard Dynamics: an Updated Survey with the Emphasis on Open Problems”, Chaos, 22:2 (2012), 026116
E. A. Gutkin, “Dinamika billiarda: obzornaya statya s aktsentom na nereshennye zadachi”, Nelineinaya dinam., 7:3 (2011), 489–512
Athreya, JS, “Deviation of ergodic averages for rational polygonal billiards”, Duke Mathematical Journal, 144:2 (2008), 285
Gorodnik, A, “Open problems in dynamics and related fields”, Journal of Modern Dynamics, 1:1 (2007), 1
Wright, P, “The periodic oscillation of an adiabatic piston in two or three dimensions”, Communications in Mathematical Physics, 275:2 (2007), 553
Samuel Lelièvre, “Siegel–Veech constants in H(2)”, Geom Topol, 10 (2006), 1157
Alonso, D, “Transport in polygonal billiards”, Physica D-Nonlinear Phenomena, 187:1–4 (2004), 184
Gutkin, E, “Billiard dynamics: A survey with the emphasis on open problems”, Regular & Chaotic Dynamics, 8:1 (2003), 1

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	664
Russian version PDF:	336
English version PDF:	30
References:	91
First page:	2

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