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March  2007, 18(2&3): 569-595. doi: 10.3934/dcds.2007.18.569

Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method

Mikhail B. Sevryuk 1,

1. 

Institute of Energy Problems of Chemical Physics, The Russia Academy of Sciences, Leninskiĭ prospect 38, Bldg. 2, Moscow 119334, Russian Federation

Received  December 2005 Revised  May 2006 Published  March 2007

We consider quasi-periodic (with $N$ basic frequencies) non-autonomous perturbations of Hamiltonian, reversible, volume preserving, and dissipative systems. The unperturbed systems possess analytic families of invariant $n$-tori carrying conditionally periodic motions, are allowed to depend on external parameters, and are assumed to satisfy just very weak nondegeneracy conditions. We construct invariant $(n+N)$-tori in perturbed systems following M.R. Herman's approach: additional external parameters are introduced to remove degeneracies and then are eliminated via an appropriate number-theoretical lemma concerning Diophantine approximations of dependent quantities.
Keywords: invariant tori, KAM theory, quasi-periodic perturbations, quasi-periodic motions, Herman's method..
Mathematics Subject Classification: 37J40, 70H08, 70K43, 70H3.
Citation: Mikhail B. Sevryuk. Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 569-595. doi: 10.3934/dcds.2007.18.569
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