Rudnev M., Wiggins, S.
KAM theory near multiplicity one resonant surfaces in
perturbations of a-priori stable Hamiltonian systems
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ABSTRACT. We consider a near-integrable Hamiltonian system in
action-angle variables with analytic Hamiltonian. For a given
resonant surface of multiplicity one we show that near a Cantor
set of points on this surface, whose remaining frequencies enjoy
the usual diophantine condition, the Hamiltonian may be written
in a simple normal form which, under certain assumptions, may
be related to the class which, following Chierchia and
Gallavotti [1994], we call {\it a-priori unstable}.
For the a-priori unstable Hamiltonian we prove a KAM-type result
for the survival of the whiskered tori under the perturbation as
an infinitely differentiable family, in the sense of Whitney,
which can then be applied to the above normal form in the
neighborhood of the whole resonant surface.