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On Totally integrable magnetic billiards on constant curvature surface
1. | School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University |
References:
[1] |
N. Berglund and H. Kunz, Integrability and ergodicity of classical billiards in a magnetic field, J. Statist. Phys., 83 (1996), 81-126.
doi: 10.1007/BF02183641. |
[2] |
M. Robnik and M. V. Berry, Classical billiards in magnetic fields, J. Phys. A, 18 (1985), 1361-1378. |
[3] |
M. Bialy, Convex billiards and a theorem by E. Hopf, Math. Z., 214 (1993), 147-154. |
[4] |
M. Bialy, Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane, arXiv:1205.3873. |
[5] |
M. L. Bialy, Rigidity for periodic magnetic fields, Ergodic Theory Dynam. Systems, 20 (2000), 1619-1626. |
[6] |
Chavel, Isaac, "Riemannian Geometry," A Modern Introduction. Cambridge Studies in Advanced Mathematics, 98. Cambridge University Press, Cambridge, 2006. |
[7] |
B. Gutkin, U. Smilansky and E. Gutkin, Hyperbolic billiards on surfaces of constant curvature, Comm. Math. Phys., 208 (1999), 65-90.
doi: 10.1007/s002200050748. |
[8] |
Gutkin, Boris Hyperbolic magnetic billiards on surfaces of constant curvature, Comm. Math. Phys., 217 (2001), 33-53. |
[9] |
E. Gutkin, Billiard dynamics: A survey with the emphasis on open problems, Regul. Chaotic Dyn., 8 (2003), 1-13. |
[10] |
E. Gutkin and S. Tabachnikov, Billiards in Finsler and Minkowski geometries, J. Geom. Phys., 40 (2002), 277-301. |
[11] |
A. Knauf, Closed orbits and converse KAM theory, Nonlinearity, 3 (1990), 961-973. |
[12] | |
[13] |
S. Tabachnikov, Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem. in "Modern Dynamical Systems and Applications" 233-250, Cambridge Univ. Press, Cambridge, 2004. |
[14] |
T. Tasnadi, The behavior of nearby trajectoriies in magnetic billiards, J. Math. Phys., 37 (1996), 5577-5598. |
[15] |
A. Veselov, Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space, J. Geom. Phys., 7 (1990), 81-107. |
[16] |
M. Wojtkowski, Two applications of Jacobi fields to the billiard ball problem, J. Differential Geom., 40 (1994), 155-164. |
show all references
References:
[1] |
N. Berglund and H. Kunz, Integrability and ergodicity of classical billiards in a magnetic field, J. Statist. Phys., 83 (1996), 81-126.
doi: 10.1007/BF02183641. |
[2] |
M. Robnik and M. V. Berry, Classical billiards in magnetic fields, J. Phys. A, 18 (1985), 1361-1378. |
[3] |
M. Bialy, Convex billiards and a theorem by E. Hopf, Math. Z., 214 (1993), 147-154. |
[4] |
M. Bialy, Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane, arXiv:1205.3873. |
[5] |
M. L. Bialy, Rigidity for periodic magnetic fields, Ergodic Theory Dynam. Systems, 20 (2000), 1619-1626. |
[6] |
Chavel, Isaac, "Riemannian Geometry," A Modern Introduction. Cambridge Studies in Advanced Mathematics, 98. Cambridge University Press, Cambridge, 2006. |
[7] |
B. Gutkin, U. Smilansky and E. Gutkin, Hyperbolic billiards on surfaces of constant curvature, Comm. Math. Phys., 208 (1999), 65-90.
doi: 10.1007/s002200050748. |
[8] |
Gutkin, Boris Hyperbolic magnetic billiards on surfaces of constant curvature, Comm. Math. Phys., 217 (2001), 33-53. |
[9] |
E. Gutkin, Billiard dynamics: A survey with the emphasis on open problems, Regul. Chaotic Dyn., 8 (2003), 1-13. |
[10] |
E. Gutkin and S. Tabachnikov, Billiards in Finsler and Minkowski geometries, J. Geom. Phys., 40 (2002), 277-301. |
[11] |
A. Knauf, Closed orbits and converse KAM theory, Nonlinearity, 3 (1990), 961-973. |
[12] | |
[13] |
S. Tabachnikov, Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem. in "Modern Dynamical Systems and Applications" 233-250, Cambridge Univ. Press, Cambridge, 2004. |
[14] |
T. Tasnadi, The behavior of nearby trajectoriies in magnetic billiards, J. Math. Phys., 37 (1996), 5577-5598. |
[15] |
A. Veselov, Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space, J. Geom. Phys., 7 (1990), 81-107. |
[16] |
M. Wojtkowski, Two applications of Jacobi fields to the billiard ball problem, J. Differential Geom., 40 (1994), 155-164. |
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