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
perturbative 
expansions and 
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.