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KAM theory without action-angle variables

Author
De La Llave, R.; González, A.; Jorba, A.; Villanueva, J.
Type of activity
Journal article
Journal
Nonlinearity
Date of publication
2005-03
Volume
18
Number
2
First page
855
Last page
895
DOI
https://doi.org/10.1088/0951-7715/18/2/020 Open in new window
URL
http://iopscience.iop.org/article/10.1088/0951-7715/18/2/020 Open in new window
Abstract
We give a proof of a KAM theorem on existence of invariant tori with a Diophantine rotation vector for Hamiltonian systems. The method of proof is based on the use of the geometric properties of Hamiltonian systems which, in particular, do not require the Hamiltonian system either to be written in action-angle variables or to be a perturbation of an integrable one. The proposed method is also useful to compute numerically invariant tori for Hamiltonian systems. We also prove a translated torus t...
Keywords
Action-angle variables, Degrees of freedom, Diophantine rotation vector, Geometric properties, Hamiltonian systems, Integrable system perturbation, Invariant tori, KAM theorem, Translated torus theorem
Group of research
EGSA - Differential Equations, Geometry, Control and Dynamical Systems, and Applications
SD - UPC Dynamical Systems

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