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.

Lindstedt series, ultraviolet divergences and Moser's theorem / Bonetto, F; Gallavotti, Giovanni; Gentile, G; Mastropietro, V.. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 26:(1998), pp. 545-593.

Lindstedt series, ultraviolet divergences and Moser's theorem

GALLAVOTTI, Giovanni;
1998

Abstract

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.
1998
MOSER THEOREM; DIFFERENTIABLE KAM; LINDSTEDT SERIES
01 Pubblicazione su rivista::01a Articolo in rivista
Lindstedt series, ultraviolet divergences and Moser's theorem / Bonetto, F; Gallavotti, Giovanni; Gentile, G; Mastropietro, V.. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 26:(1998), pp. 545-593.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/6179
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