93-6 R.de la Llave , S.Tompaidis

Computation of Domains of Analyticity for some Perturbative Expansions of Mechanics (309K, TeX with PS figures) Jan 12, 93

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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.

Files: 93-6.tex