The first derivative of the period function of a plane vector field

• Autores: Jean-Pierre Françoise
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 1, 1997 (Ejemplar dedicado a: Proceedings of the Symposium on Planar Vector Fields), págs. 127-134
• Idioma: inglés
• Títulos paralelos:
  • La primera derivada de la función del período de un campo vectorial plano
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• Resumen

  • The algorithm of the successive derivatives introduced in \cite{5} was implemented in \cite{7}, \cite{8}. This algorithm is based on the existence of a decomposition of 1-forms associated to the relative cohomology of the Hamiltonian function which is perturbed. We explain here how the first step of this algorithm gives also the first derivative of the period function. This includes, for instance, new presentations of formulas obtained by Carmen Chicone and Marc Jacobs in \cite{3}.