%0 Journal Article
%D 2014
%T An Abstract Nashâ€“Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds
%A Massimiliano Berti
%A Livia Corsi
%A Michela Procesi
%X 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.
%I Springer
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34651
%1 34858
%2 Mathematics
%$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:19:54Z
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%R 10.1007/s00220-014-2128-4