### Absolutely convergent series expansions for quasi periodic motions.

Eliasson, L.H. (1996)

Mathematical Physics Electronic Journal [electronic only]

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Eliasson, L.H. (1996)

Mathematical Physics Electronic Journal [electronic only]

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Ricardo Pérez-Marco (2001-2002)

Séminaire Bourbaki

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Massimiliano Berti (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in ${\mathbb{T}}^{d}$, $d\ge 2$, and the $1$-$d$ derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.

Yiming Long (1990)

Mathematische Zeitschrift

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M. Timoumi, A. Trad (1995)

Collectanea Mathematica

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Bambusi, Dario, Gaeta, Giuseppe (2002)

Mathematical Physics Electronic Journal [electronic only]

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Chengfu Che, Xiaoping Xue (2012)

Annales Polonici Mathematici

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Two theorems about the existence of periodic solutions with prescribed energy for second order Hamiltonian systems are obtained. One gives existence for almost all energies under very natural conditions. The other yields existence for all energies under a further condition.

A. Katok, D. Bernstein (1987)

Inventiones mathematicae

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Klaus Thews (1980/81)

Manuscripta mathematica

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Zhang, Dongfeng, Cheng, Rong (2010)

Fixed Point Theory and Applications [electronic only]

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Thomas Bartsch, Michel Willem (1994)

Journal für die reine und angewandte Mathematik

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Massimiliano Berti, Luca Biasco, Enrico Valdinoci (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period...