Abstract
A general direct method, alternative to KAM theory, apt to deal with small divisor problems in the real-analytic category, is presented and tested on several small divisor problems including the construction of maximal quasi-periodic solutions for nearly-integrable non-degenerate Hamiltonian or Lagrangian systems and the construction of lower dimensional resonant tori for nearly-integrable Hamiltonian systems. The method is based on an explicit graph theoretical representation of the formal power series solutions, which allows to prove compensations among the monomials forming such representation.
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Communicated by J.-P. Eckmann
L.C. thanks C. Simó and theCentre de Recerca Matemàtica (Bellaterra) for kind hospitality; he also acknowledges partial support by CNR-GNAFA. The authors gratefully acknowledge helpful discussions with C. Liverani.
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Chierchia, L., Falcolini, C. Compensations in small divisor problems. Commun.Math. Phys. 175, 135–160 (1996). https://doi.org/10.1007/BF02101627
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DOI: https://doi.org/10.1007/BF02101627