A. N. Zemlyakov, A. B. Katok, “Topological transitivity of billiards in polygons”, Mat. Zametki, 18:2 (1975), 291–300; Math. Notes, 18:2 (1975), 760

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Matematicheskie Zametki, 1975, Volume 18, Issue 2, Pages 291–300 (Mi mzm7652)

This article is cited in 114 scientific papers (total in 114 papers)

Topological transitivity of billiards in polygons

A. N. Zemlyakov^a, A. B. Katok^b

^a M. V. Lomonosov Moscow State University
^b Central Economics and Mathematics Institute, USSR Academy of Sciences

Full-text PDF (998 kB) Citations (114)

Abstract: Consider a billiard in a polygon $Q\subset R^2$ having all angles commensurate with $\pi$. For the majority of initial directions, density of every infinite semitrajectory in configuration space is proved. Also proved is the typicality of polygons for which some billiard trajectory is dense in phase space.

Received: 26.09.1974

English version:
Mathematical Notes, 1975, Volume 18, Issue 2, Pages 760–764
DOI: https://doi.org/10.1007/BF01818045

Bibliographic databases:

UDC: 513.83

Language: Russian

Citation: A. N. Zemlyakov, A. B. Katok, “Topological transitivity of billiards in polygons”, Mat. Zametki, 18:2 (1975), 291–300; Math. Notes, 18:2 (1975), 760–764

Citation in format AMSBIB

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\paper Topological transitivity of billiards in polygons

\jour Mat. Zametki

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\pages 291--300

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\zmath{https://zbmath.org/?q=an:0315.58014}

\transl

\jour Math. Notes

\yr 1975

\vol 18

\issue 2

\pages 760--764

\crossref{https://doi.org/10.1007/BF01818045}

Linking options:

https://www.mathnet.ru/eng/mzm7652

https://www.mathnet.ru/eng/mzm/v18/i2/p291

Erratum

Letter to the editor
A. N. Zemlyakov, A. B. Katok
Mat. Zametki, 1976, 20:6, 883

This publication is cited in the following 114 articles:

Vijay Balasubramanian, Rathindra Nath Das, Johanna Erdmenger, Zhuo-Yu Xian, “Chaos and integrability in triangular billiards”, J. Stat. Mech., 2025:3 (2025), 033202
Črt Lozej, Eugene Bogomolny, “Intermediate spectral statistics of rational triangular quantum billiards”, Phys. Rev. E, 110:2 (2024)
Giovanni Forni, Lecture Notes in Mathematics, 2347, Modern Aspects of Dynamical Systems, 2024, 161
Pradeep Singh, “Coding Billiards in Hyperbolic 3-Space”, J Dyn Control Syst, 30:4 (2024)
Garima Rajpoot, Komal Kumari, Sudhir Ranjan Jain, “Quantum error correction beyond the toric code: dynamical systems meet encoding”, Eur. Phys. J. Spec. Top., 2023
James F. Peters, Advances in Intelligent Systems and Computing, 1437, Applied Nonlinear Analysis and Soft Computing, 2023, 419
József Beck, William W. L. Chen, “Generalization of a density theorem of Khinchin and diophantine approximation”, Journal de théorie des nombres de Bordeaux, 35:2 (2023), 511
Eugene Bogomolny, “Random matrices associated with general barrier billiards”, J. Phys. A: Math. Theor., 55:25 (2022), 254002
J. Beck, W. W. L. Chen, Y. Yang, “Quantitative behavior of non-integrable systems. III”, Acta Math. Hungar., 166:2 (2022), 254
Jayadev S. Athreya, David Aulicino, W. Patrick Hooper, “Platonic Solids and High Genus Covers of Lattice Surfaces”, Experimental Mathematics, 31:3 (2022), 847
Eugene Bogomolny, “Level Compressibility of Certain Random Unitary Matrices”, Entropy, 24:6 (2022), 795
Barbara Dietz, Achim Richter, “Intermediate statistics in singular quarter-ellipse shaped microwave billiards*”, J. Phys. A: Math. Theor., 55:31 (2022), 314001
Eugene Bogomolny, “Barrier billiard and random matrices”, J. Phys. A: Math. Theor., 55:2 (2022), 024001
Dmitry Fuchs, “Billiard Trajectories in Regular Polygons and Geodesics on Regular Polyhedra”, Arnold Math J., 7:4 (2021), 493
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
İsmail SAĞLAM, Ahmet Refah Torun, “Düz Disklerdeki Bilardo Akışlar{\i}n{\i}n Topolojik Geçişliliği”, Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 7 (2020), 295
Efim B. Rozenbaum, Leonid A. Bunimovich, Victor Galitski, “Early-Time Exponential Instabilities in Nonchaotic Quantum Systems”, Phys. Rev. Lett., 125:1 (2020)
J. Beck, M. Donders, Y. Yang, “Quantitative behavior of non-integrable systems. I”, Acta Math. Hungar., 161:1 (2020), 66
Yumin Zhong, “On the Areas of the Minimal Triangles in Veech Surfaces”, Acta Math Sci, 40:2 (2020), 503
Krzysztof Frączek, “Ergodic properties of the ideal gas model for infinite billiards”, Physica D: Nonlinear Phenomena, 390 (2019), 9

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

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