- 01-73 Jean Bricmont, Antti Kupiainen, Alain Schenkel
- Renormalization Group and the Melnikov Problem for PDE's
(128K, plain TeX)
Feb 23, 01
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Abstract. We give a new proof of persistence of quasi-periodic, low dimensional
elliptic tori in infinite dimensional systems. The proof is based on a
renormalization group iteration that was developed recently in [BGK] to
address the standard KAM problem, namely, persistence of invariant
tori of maximal dimension in finite dimensional, near integrable systems.
Our result covers situations in which the so called normal frequencies
are multiple. In particular, it provides a new proof of the existence of
small-amplitude, quasi-periodic solutions of nonlinear wave equations
with periodic boundary conditions.