Lindstedt series, ultraviolet divergences and Moser's theorem

• Federico Bonetto ^[1] ; Giovanni Gallavotti ^[1] ; Guido Gentile ^[2] ; Vieri Mastropietro ^[3]
  1. [1] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
  2. [2] IHES Bures sur Yvette, France
  3. [3] Università di Roma II, Italia

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 26, Nº 3, 1998, págs. 545-593
• Idioma: inglés
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• Resumen

  • Moser’s invariant tori for a class of nonanalytic quasi integrable even Hamiltonian systems are shown to be analytic in the perturbation parameter. We do so by exhibiting a summation rule for the divergent series ("Lindstedt series") that formally define them. We find additional cancellations taking place in the formal series, besides the ones already known and necessary in the analytic case (i.e. to prove convergence of Lindtsedt algorithm for Kolmogorov’s invariant tori).

    The method is interpreted in terms of a non renormalizable quantum field theory, considerably more singular than the one we pointed out in the analytic case.