Results 1 to 10 of about 1,567 (48)

Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems [PDF]

, 1996
Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting.
A. J. Lichtenberg, B. Eckhardt, D. Bambusi, D. Farelly, E. L. Sibert III, G. Falk, G. Falk, G. Wentzel, H. R. Jauslin, I. Shavitt, J. Bellissard, J. R. Cary, L. E. Fried, M. Cibils, M. Robnik, M. V. Berry, N. Srivastava, O. Bohigas, P. A. M. Dirac, P. Crehan, R. G. Newton, S. Graffi, St. Weigert, St. Weigert, Stefan Weigert, T. Uzer, Thomas Gramespacher, W. Heisenberg, W. R. Greenberg, W. Thirring   +29 more
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A new approach to the parameterization method for Lagrangian tori of hamiltonian systems [PDF]

, 2016
We compute invariant Lagrangian tori of analytic Hamiltonian systems by the parameterization method. Under Kolmogorov’s non-degeneracy condition, we look for an invariant torus of the system carrying quasi-periodic motion with fixed frequencies.
Villanueva Castelltort, Jordi
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Generic perturbations of linear integrable Hamiltonian systems [PDF]

, 2015
In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invariant tori), the Nekhoroshev theorem (stability of the action variables for a
A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Bounemoura, A. Morbidelli, A.N. Kolmogorov, Abed Bounemoura, B.V. Chirikov, F. Fassò, G. Popov, J. Moser, J. Pöschel, J. Pöschel, L. Biasco, M. B. Sevryuk, N. N. Nekhoroshev, N. N. Nekhoroshev, N. N. Nekhoroshev, R. Douady, V. I. Arnold, V. I. Arnol’d, V. I. Arnol’d   +26 more
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Double exponential stability of quasi-periodic motion in Hamiltonian systems [PDF]

, 2016
We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval ...
A. Bounemoura, A. Bounemoura, A. Giorgilli, A. Knauf, A. Morbidelli, A.G. Medvedev, A.I. Neishtadt, Abed Bounemoura, Bassam Fayad, D. Bambusi, G. Popov, H. Ito, J. Bochnak, L.H. Eliasson, Laurent Niederman, N.N. Nekhoroshev, N.N. Nekhoroshev, R. Douady, T. Mitev   +18 more
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What makes nonholonomic integrators work? [PDF]

, 2020
A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example.
Modin, Klas, Verdier, Olivier
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The classical KAM theorem for Hamiltonian systems via rational approximations

, 2014
In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate Hamiltonian systems close to ...
Bounemoura, Abed, Fischler, Stephane
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Analytic Lagrangian tori for the planetary many-body problem

, 2009
In 2004, F\'ejoz [D\'emonstration du 'th\'eor\'eme d'Arnold' sur la stabilit\'e du syst\`eme plan\'etaire (d'apr\`es M. Herman). Ergod. Th. & Dynam. Sys.
Arnol’d, Celletti, FABIO PUSATERI, LUIGI CHIERCHIA, Poincaré, Salamon, Sevryuk   +6 more
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A Cantor set of tori with monodromy near a focus-focus singularity

, 2003
We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus ...
Bob Rink, Broer H W, Broer H W Cushman R H Fasso F, Cushman R H, Cushman R H, Duistermaat J J, Eliasson L H, Faure F, Horozov E, Lazutkin V F, Matveev V S, Pöschel J, Steenrod N   +12 more
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The Dynamics of Three-Planet Systems: an Approach from Dynamical System

, 2010
We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading to highly ...
Arnol'd, Bungo Shikita, Butler, Ford, Hiroko Koyama, Juric, Kokubo, Kolmogorov, Leichl, Shen, Shoichi Yamada, Zhou   +11 more
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Resonance-Assisted Tunneling [PDF]

, 2002
We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is
Arnold, Barnas, Bogomolny, Bohigas, Bohigas, Bonci, Breuer, Brodier, Chirikov, Creagh, Creagh, Creagh, Davis, Dembowski, Denis Ullmo, Doron, Farrely, Frischat, Geisel, Greene, Grossmann, Hensinger, Landau, Langer, Leboeuf, Leyvraz, Lichtenberg, Lima, Lin, Maslov, Moser, Mouchet, Nöckel, Olivier Brodier, Onishi, Ozorio de Almeida, Peter Schlagheck, Roncaglia, Shudo, Shudo, Shudo, Sokolov, Sokolov, Steck, Steck, Tomsovic, Uzer, Wilkinson, Wilkinson, Zakrzewski   +49 more
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