 1461 Massimiliano Berti, Philippe Bolle
 A NashMoser approach to KAM theory
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Jul 28, 14

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Abstract. Any finite dimensional embedded invariant torus of an Hamiltonian system,
densely filled by quasiperiodic solutions, is isotropic. This property allows us
to construct a set of symplectic coordinates in a neighborhood of the torus in which
the Hamiltonian is in a generalized KAM normal form with angledependent coefficients.
Based on this observation we develop an approach to KAM theory via
a NashMoser implicit function iterative theorem. The key point is to construct an
approximate right inverse of the differential operator associated to the linearized
Hamiltonian system at each approximate quasiperiodic solution. In the above symplectic
coordinates the linearized dynamics on the tangential and normal directions
to the approximate torus are approximately decoupled. The construction of an approximate
inverse is thus reduced to solving a quasiperiodically forced linear differential
equation in the normal variables. Applications of this procedure allow to
prove the existence of finite dimensional Diophantine invariant tori of autonomous
PDE's
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