  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.
