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Mathematics > Dynamical Systems

arXiv:math/0405420 (math)
[Submitted on 21 May 2004]

Title:Degenerate elliptic resonances

Authors:Guido Gentile Giovanni Gallavotti
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Abstract: Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed as formal power series in the perturbation parameter and can be given a meaning via resummations. Here we prove that, for a class of elliptic tori, a resummation algorithm can be devised and proved to be convergent, thus extending to such lower-dimensional invariant tori the methods employed to prove convergence of the Lindstedt series either for the maximal (i.e. KAM) tori or for the hyperbolic lower-dimensional invariant tori.
Subjects: Dynamical Systems (math.DS)
Report number: FM 06-04
Cite as: arXiv:math/0405420 [math.DS]
  (or arXiv:math/0405420v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.math/0405420

Submission history

From: Giovanni Gallavotti [view email]
[v1] Fri, 21 May 2004 17:12:43 UTC (56 KB)
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