On Poincaré's Fourth and Fifth Examples of Limit Cycles at Infinity

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dc.creatorRoeder, Roland K. W.
dc.date2006-01-10
dc.date.accessioned2026-07-07T06:58:42Z
dc.date.available2026-07-07T06:58:42Z
dc.descriptionErrors are found in example problems from Henri Poincaré's paper ``Mémoire sur les courbes définies par une équation différentielle.'' Examples four and five from chapter seven and examples one, two, and three from chapter nine do not have the limit cycles at infinity predicted by Poincaré. Instead they have fixed points at every point at infinity. In order to understand the errors made by Poincaré, examples four and five are studied at length. Replacement equations for the fourth and fifth examples are suggested based on the supposition that terms were omitted from Poincaré's equations.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0601204
dc.identifierhttp://arxiv.org/abs/math/0601204
dc.identifierRocky Mountain Journal of Mathematics, 33 (3): 1057-1082, 2003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107462
dc.subjectDynamical Systems
dc.subjectHistory and Overview
dc.subject37C10; 34C04; 34C07
dc.titleOn Poincaré's Fourth and Fifth Examples of Limit Cycles at Infinity
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