@article {2014,
title = {An Abstract Nash{\textendash}Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds},
number = {Communications in mathematical physics;volume 334; issue 3; pages 1413-1454;},
year = {2014},
publisher = {Springer},
abstract = {We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.},
doi = {10.1007/s00220-014-2128-4},
url = {http://urania.sissa.it/xmlui/handle/1963/34651},
author = {Massimiliano Berti and Livia Corsi and Michela Procesi}
}