Extension of Bautin Theory to Any Dimension

• Autores: Jean-Pierre Françoise
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 2, Nº 1, 2001, págs. 145-150
• Idioma: español
• DOI: 10.1007/bf02969387
• Texto completo no disponible (Saber más ...)
• Resumen

  • Bautin made some years ago a decisive contribution to the algebraic approach of the perturbation theory of periodic orbits of plane polynomial vector fields. This article presents first steps of a general framework in which a generalization of Bautin's ideas to any dimension could be developed. The main result is the generalization of the algorithm of the successive derivatives of return mappings for $2$-dimensional systems to any dimension in this framework.