- 95-506 Bonetto, F., Gallavotti, G., Gentile, G., Mastropietro, V.
- Lindstedt series, ultraviolet divergences and Moser's theorem
(466K, Postscript, uncompressed)
Nov 28, 95
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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 (\ie 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