Ref HAL: hal-00420854_v1
Ref Arxiv: 0909.5574
DOI: 10.1088/1751-8113/43/8/085207
Ref. & Cit.: NASA ADS
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Résumé:

We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These expansions are of the so--called weak Painlevé type. However, in view of these expansions, it is not possible to distinguish between integrable and non integrable cases.