S. Troubetzkoy, “Recurrence and periodic billiard orbits in polygons”, Regul. Chaotic Dyn., 9:1 (2004), 1

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Regular and Chaotic Dynamics, 2004, Volume 9, Issue 1, Pages 1–12
DOI: https://doi.org/10.1070/RD2004v009n01ABEH000259 (Mi rcd725)

This article is cited in 12 scientific papers (total in 12 papers)

Recurrence and periodic billiard orbits in polygons

S. Troubetzkoy

Centre de Physique Théorique, Institut de Mathématiques de Luminy et Federation de Recherches des Unites de Mathematiques de Marseille, CNRS Luminy, Case 907, F-13288 Marseille Cedex 9, France

Citations (12)

DOI: https://doi.org/10.1070/RD2004v009n01ABEH000259

Abstract: We show that almost all billiard trajectories return parallel to themselves for rank

1

$1$ , ergodic polygons. Applications are given to the existence of periodic trajectories.

Received: 08.01.2004

Bibliographic databases:

Document Type: Article

MSC: 37A40, 37C05, 37C27

Language: English

Citation: S. Troubetzkoy, “Recurrence and periodic billiard orbits in polygons”, Regul. Chaotic Dyn., 9:1 (2004), 1–12

Citation in format AMSBIB

\Bibitem{Tro04}

\by S. Troubetzkoy

\paper Recurrence and periodic billiard orbits in polygons

\jour Regul. Chaotic Dyn.

\yr 2004

\vol 9

\issue 1

\pages 1--12

\mathnet{http://mi.mathnet.ru/rcd725}

\crossref{https://doi.org/10.1070/RD2004v009n01ABEH000259}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2058893}

\zmath{https://zbmath.org/?q=an:1049.37024}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9....1T}

Linking options:

https://www.mathnet.ru/eng/rcd725

https://www.mathnet.ru/eng/rcd/v9/i1/p1

This publication is cited in the following 12 articles:

Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just, “Non-periodic not everywhere dense trajectories in triangular billiards”, Trans. Amer. Math. Soc., 2024
Katerina Zahradova, Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just, “Anomalous dynamics in symmetric triangular irrational billiards”, Physica D: Nonlinear Phenomena, 445 (2023), 133619
Zaijong Hwang, Christoph A. Marx, Joseph J. Seaward, Svetlana Jitomirskaya, Maxim Olshanii, “Growth of the Wang-Casati-Prosen counter in an integrable billiard”, SciPost Phys., 14:2 (2023)
Jozef Bobok, Serge Troubetzkoy, “Topologically weakly mixing polygonal billiards”, Proc. Amer. Math. Soc., 2023
Yang Shen, Jiazhong Yang, “Hearing the shape of right triangle billiard tables”, DCDS, 41:12 (2021), 5537
W Patrick Hooper, “The invariant measures of some infinite interval exchange maps”, Geom. Topol., 19:4 (2015), 1895
John A. Toth, Steve Zelditch, “Quantum Ergodic Restriction Theorems. I: Interior Hypersurfaces in Domains with Ergodic Billiards”, Ann. Henri Poincaré, 13:4 (2012), 599
Jozef Bobok, Serge Troubetzkoy, “Code and order in polygonal billiards”, Topology and its Applications, 159:1 (2012), 236
Serge Troubetzkoy, “Recurrence in generic staircases”, Discrete & Continuous Dynamical Systems - A, 32:3 (2012), 1047
Pascal Hubert, Samuel Lelièvre, Serge Troubetzkoy, “The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2011:656 (2011)
B. Cooley, P. K. Newton, “Eigenvalue Distributions from Impacts on a Ring”, Regul. Chaotic Dyn., 12:1 (2007), 12–26
S. Troubetzkoy, J. Schmeling, “Inhomogeneous Diophantine approximation and angular recurrence for polygonal billiards”, Sb. Math., 194:2 (2003), 295–309

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

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