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R.de la Llave , S.Tompaidis
Computation of Domains of Analyticity
for some Perturbative Expansions of Mechanics
(309K, TeX with PS figures)
ABSTRACT. We compute the domain of analyticity
of some perturbative expansions for invariant circles
appearing in mechanics. We use Pad\'e approximants for the
introduce methods to ascertain their domain of convergence.
We also use non-perturbative methods based on direct
computation of the invariant circles
and, in analogy with Greene's criterion, approximation by
circles with rational rotation.
We find that the domains computed by all the methods agree within
the limits of accuracy. The analytic structure of the expansions
for rational frequencies is clarified rigorously.