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Lower bounds on growth rates of periodic billiard trajectories in some irrational polygons
1. | Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208-2730, United States |
[1] |
Ferrán Valdez. Veech groups, irrational billiards and stable abelian differentials. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 1055-1063. doi: 10.3934/dcds.2012.32.1055 |
[2] |
Michel L. Lapidus, Robert G. Niemeyer. Sequences of compatible periodic hybrid orbits of prefractal Koch snowflake billiards. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3719-3740. doi: 10.3934/dcds.2013.33.3719 |
[3] |
Dmitri Scheglov. Growth of periodic orbits and generalized diagonals for typical triangular billiards. Journal of Modern Dynamics, 2013, 7 (1) : 31-44. doi: 10.3934/jmd.2013.7.31 |
[4] |
Kai Tao. Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1495-1533. doi: 10.3934/dcds.2021162 |
[5] |
Daniel Genin, Serge Tabachnikov. On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards. Journal of Modern Dynamics, 2007, 1 (2) : 155-173. doi: 10.3934/jmd.2007.1.155 |
[6] |
Bettina Klaus, Frédéric Payot. Paths to stability in the assignment problem. Journal of Dynamics and Games, 2015, 2 (3&4) : 257-287. doi: 10.3934/jdg.2015004 |
[7] |
Tony Lyons. Particle paths in equatorial flows. Communications on Pure and Applied Analysis, 2022, 21 (7) : 2399-2414. doi: 10.3934/cpaa.2022041 |
[8] |
Nicolas Bedaride. Entropy of polyhedral billiard. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 89-102. doi: 10.3934/dcds.2007.19.89 |
[9] |
Pavel Bachurin, Konstantin Khanin, Jens Marklof, Alexander Plakhov. Perfect retroreflectors and billiard dynamics. Journal of Modern Dynamics, 2011, 5 (1) : 33-48. doi: 10.3934/jmd.2011.5.33 |
[10] |
Qinglan Xia. On landscape functions associated with transport paths. Discrete and Continuous Dynamical Systems, 2014, 34 (4) : 1683-1700. doi: 10.3934/dcds.2014.34.1683 |
[11] |
David Cowan. A billiard model for a gas of particles with rotation. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 101-109. doi: 10.3934/dcds.2008.22.101 |
[12] |
Mason A. Porter, Richard L. Liboff. The radially vibrating spherical quantum billiard. Conference Publications, 2001, 2001 (Special) : 310-318. doi: 10.3934/proc.2001.2001.310 |
[13] |
David Cowan. Rigid particle systems and their billiard models. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 111-130. doi: 10.3934/dcds.2008.22.111 |
[14] |
W. Patrick Hooper, Richard Evan Schwartz. Billiards in nearly isosceles triangles. Journal of Modern Dynamics, 2009, 3 (2) : 159-231. doi: 10.3934/jmd.2009.3.159 |
[15] |
Serge Tabachnikov. Birkhoff billiards are insecure. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1035-1040. doi: 10.3934/dcds.2009.23.1035 |
[16] |
Simon Castle, Norbert Peyerimhoff, Karl Friedrich Siburg. Billiards in ideal hyperbolic polygons. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 893-908. doi: 10.3934/dcds.2011.29.893 |
[17] |
Timothy Chumley, Renato Feres. Entropy production in random billiards. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1319-1346. doi: 10.3934/dcds.2020319 |
[18] |
Richard Evan Schwartz. Outer billiards and the pinwheel map. Journal of Modern Dynamics, 2011, 5 (2) : 255-283. doi: 10.3934/jmd.2011.5.255 |
[19] |
Mickaël Kourganoff. Uniform hyperbolicity in nonflat billiards. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1145-1160. doi: 10.3934/dcds.2018048 |
[20] |
Qinglan Xia. An application of optimal transport paths to urban transport networks. Conference Publications, 2005, 2005 (Special) : 904-910. doi: 10.3934/proc.2005.2005.904 |
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