On invariant tori of nearly integrable Hamiltonian systems with quasiperiodic perturbation.
Zhang, Dongfeng, Cheng, Rong (2010)
Fixed Point Theory and Applications [electronic only]
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Zhang, Dongfeng, Cheng, Rong (2010)
Fixed Point Theory and Applications [electronic only]
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Jürgen Pöschel (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Pierre Lochak, Jean-Pierre Marco (2005)
Open Mathematics
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For a positive integer n and R>0, we set . Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian on , with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of , and setting the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly...
de la Llave, R., Wayne, C.E. (2004)
Mathematical Physics Electronic Journal [electronic only]
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Jean-Pierre Marco, David Sauzin (2003)
Publications Mathématiques de l'IHÉS
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R. Dieckerhoff, E. Zehnder (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Bambusi, Dario, Gaeta, Giuseppe (2002)
Mathematical Physics Electronic Journal [electronic only]
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Dario Bambusi (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We use the Galerkin averaging method to construct a coordinate transformation putting a nonlinear PDE in Poincaré normal form up to finite order. We also give a rigorous estimate of the remainder showing that it is small as a differential operator of very high order. The abstract theorem is then applied to a quasilinear wave equation, to the water wave problem and to a nonlinear heat equation. The normal form is then used to construct approximate solutions whose difference from true...