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

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  • 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.
    Mathematics Subject Classification: 37J40, 70H08, 70K43, 70H33.

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