Lindstedt series, ultraviolet divergences and Moser's theorem

Details Lindstedt series, ultraviolet divergences and Moser's theorem Lindstedt series, ultraviolet divergences and Moser's theorem

1995-11-28

arxiv.org/abs/chao-dyn/9511009v1

Annali della Scuola Normale Superiore di Pisa, 26, 545--593, 1998

Nonlinear Sciences

Chaotic Dynamics

38 pages, postscript, compressed

Scientific paper

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.

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