I. K. Babenko, “Periodic trajectories in three-dimensional Birkhoffs billiards”, Math. USSR-Sb., 71:1 (1992), 1

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Mathematics of the USSR-Sbornik, 1992, Volume 71, Issue 1, Pages 1–13
DOI: https://doi.org/10.1070/SM1992v071n01ABEH001273 (Mi sm1214)

This article is cited in 10 scientific papers (total in 10 papers)

Periodic trajectories in three-dimensional Birkhoffs billiards

I. K. Babenko

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

English version PDF (836 kB) Citations (10) Russian version article

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DOI: https://doi.org/10.1070/SM1992v071n01ABEH001273

Abstract: A lower bound is given for the number of periodic trajectories inside a strictly convex domain in three dimensional space.

Received: 16.01.1989

Bibliographic databases:

UDC: 517.974.8

MSC: Primary 58F22, 57R70; Secondary 53A17

Language: English

Original paper language: Russian

Citation: I. K. Babenko, “Periodic trajectories in three-dimensional Birkhoffs billiards”, Math. USSR-Sb., 71:1 (1992), 1–13

Citation in format AMSBIB

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\by I.~K.~Babenko

\paper Periodic trajectories in three-dimensional Birkhoffs billiards

\jour Math. USSR-Sb.

\yr 1992

\vol 71

\issue 1

\pages 1--13

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Linking options:

https://www.mathnet.ru/eng/sm1214

https://doi.org/10.1070/SM1992v071n01ABEH001273

https://www.mathnet.ru/eng/sm/v181/i9/p1155

This publication is cited in the following 10 articles:

Pavle V. M. Blagojević, Michael Harrison, S. Tabachnikov, Günter M. Ziegler, “Counting Periodic Trajectories of Finsler Billiards”, SIGMA, 16 (2020), 022, 33 pp.
Suresh Eswarathasan, Iosif Polterovich, John A. Toth, “Smooth Billiards with a Large Weyl Remainder”, Int Math Res Notices, 2016:12 (2016), 3639
Pablo S. Casas, Rafael Ramírez-Ros, “Classification of symmetric periodic trajectories in ellipsoidal billiards”, Chaos, 22:2 (2012), 026110
Pablo S. Casas, Rafael Ramirez-Ros, “The Frequency Map for Billiards inside Ellipsoids”, SIAM J. Appl. Dyn. Syst, 10:1 (2011), 278
Mazzucchelli M., “On the Multiplicity of Non-Iterated Periodic Billiard Trajectories”, Pac. J. Math., 252:1 (2011), 181–205
Karasev R.N., “Periodic Billiard Trajectories in Smooth Convex Bodies”, Geom. Funct. Anal., 19:2 (2009), 423–428
R. N. Karasev, “Topological methods in combinatorial geometry”, Russian Math. Surveys, 63:6 (2008), 1031–1078
Michael Farber, Serge Tabachnikov, “Topology of cyclic configuration spaces and periodic trajectories of multi-dimensional billiards”, Topology, 41:3 (2002), 553
Michael Farber, “Topology of billiard problems, II”, Duke Math. J., 115:3 (2002)
Michael Farber, “Topology of billiard problems, I”, Duke Math. J., 115:3 (2002)

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

Statistics & downloads:
Abstract page:	488
Russian version PDF:	137
English version PDF:	144
References:	77
First page:	4

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