Gevrey normal form and effective stability of Lagrangian tori

Todor Mitev; Georgi Popov

doi:10.3934/dcdss.2010.3.643

Article Contents

2010, Volume 3, Issue 4: 643-666. Doi: 10.3934/dcdss.2010.3.643

This issue Previous Article Convergence of differentiable functions on closed sets and remarks on the proofs of the "Converse Approximation Lemmas'' Next Article Finite smooth normal forms and integrability of local families of vector fields

Gevrey normal form and effective stability of Lagrangian tori

Todor Mitev^1, and
Georgi Popov^2,

1.
University of Rousse, Department of Algebra and Geometry, 7012, Rousse
2.
Université de Nantes, Laboratoire de mathématiques Jean Leray, 2, rue de la Houssinière, BP 92208, 44072 Nantes Cedex 03

Received: March 31, 2009

Revised: May 31, 2010

Published: November 2010

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Abstract

A Gevrey symplectic normal form of an analytic and more generally Gevrey smooth Hamiltonian near a Lagrangian invariant torus with a Diophantine vector of rotation is obtained. The normal form implies effective stability of the quasi-periodic motion near the torus.

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Mathematics Subject Classification: Primary 70H08; Secondary: 53C35.

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