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Maximizing orbits for higher-dimensional convex billiards
1. | Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Israel |
[1] |
Bassam Fayad. Discrete and continuous spectra on laminations over Aubry-Mather sets. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 823-834. doi: 10.3934/dcds.2008.21.823 |
[2] |
Ugo Bessi. Viscous Aubry-Mather theory and the Vlasov equation. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 379-420. doi: 10.3934/dcds.2014.34.379 |
[3] |
Hans Koch, Rafael De La Llave, Charles Radin. Aubry-Mather theory for functions on lattices. Discrete and Continuous Dynamical Systems, 1997, 3 (1) : 135-151. doi: 10.3934/dcds.1997.3.135 |
[4] |
Fabio Camilli, Annalisa Cesaroni. A note on singular perturbation problems via Aubry-Mather theory. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 807-819. doi: 10.3934/dcds.2007.17.807 |
[5] |
Artur O. Lopes, Rafael O. Ruggiero. Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1155-1174. doi: 10.3934/dcds.2011.29.1155 |
[6] |
Yasuhiro Fujita, Katsushi Ohmori. Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2009, 8 (2) : 683-688. doi: 10.3934/cpaa.2009.8.683 |
[7] |
Diogo A. Gomes. Viscosity solution methods and the discrete Aubry-Mather problem. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 103-116. doi: 10.3934/dcds.2005.13.103 |
[8] |
Siniša Slijepčević. The Aubry-Mather theorem for driven generalized elastic chains. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2983-3011. doi: 10.3934/dcds.2014.34.2983 |
[9] |
Kaizhi Wang, Lin Wang, Jun Yan. Aubry-Mather theory for contact Hamiltonian systems II. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 555-595. doi: 10.3934/dcds.2021128 |
[10] |
Alfonso Sorrentino. Computing Mather's $\beta$-function for Birkhoff billiards. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 5055-5082. doi: 10.3934/dcds.2015.35.5055 |
[11] |
Hong-Kun Zhang. Free path of billiards with flat points. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4445-4466. doi: 10.3934/dcds.2012.32.4445 |
[12] |
Richard Evan Schwartz. Unbounded orbits for outer billiards I. Journal of Modern Dynamics, 2007, 1 (3) : 371-424. doi: 10.3934/jmd.2007.1.371 |
[13] |
Anulekha Dhara, Aparna Mehra. Conjugate duality for generalized convex optimization problems. Journal of Industrial and Management Optimization, 2007, 3 (3) : 415-427. doi: 10.3934/jimo.2007.3.415 |
[14] |
Daniel Genin. Research announcement: Boundedness of orbits for trapezoidal outer billiards. Electronic Research Announcements, 2008, 15: 71-78. doi: 10.3934/era.2008.15.71 |
[15] |
Richard Evan Schwartz. Research announcement: unbounded orbits for outer billiards. Electronic Research Announcements, 2007, 14: 1-6. doi: 10.3934/era.2007.14.1 |
[16] |
Misha Bialy. Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane. Discrete and Continuous Dynamical Systems, 2013, 33 (9) : 3903-3913. doi: 10.3934/dcds.2013.33.3903 |
[17] |
Roland Hildebrand. Barriers on projective convex sets. Conference Publications, 2011, 2011 (Special) : 672-683. doi: 10.3934/proc.2011.2011.672 |
[18] |
Thomas Dauer, Marlies Gerber. Generic absence of finite blocking for interior points of Birkhoff billiards. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4871-4893. doi: 10.3934/dcds.2016010 |
[19] |
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 |
[20] |
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 |
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