- 96-318 Ichtiaroglou S., Meletlidou E.
- Psi-series and obstructions to integrability of periodically
perturbed one degree of freedom Hamiltonians
Jun 26, 96
(auto. generated ps),
of related papers
Abstract. A connection between the $\Psi$-series local expansion of the solution of
a perturbed system of O.D.E.'s and the evaluation of the Mel'nikov vector with
the method of residues has recently been found by Goriely and Tabor. By following
an analogous procedure, we find a straightforward relation between the failure of the
compatibility condition of the Painlev\'e test and the absence of an
analytic integral for periodically perturbed Hamiltonians
whose unperturbed part does not necessarily possess a
homoclinic loop. We apply these results to a periodically
perturbed unharmonic oscillator.