The first derivative of the period function of a plane vector field
type: Item
instance of: scholarly article
title: The first derivative of the period function of a plane vector field
zbMATH Open document ID: 0892.34023
DOI: 10.5565/PUBLMAT_41197_07
published in: Publicacions Matemàtiques
publication date: 1998-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/41286
review text: An algorithm to compute the derivatives of the Poincaré return map introduced in [\textit{J.-P. Françoise}, Ergodic Theory Dyn. Syst. 16, No. 1, 87-96 (1996; Zbl 0852.34008)] is used to compute the first nonzero derivative of the period function. The algorithm is somewhat different from traditional power series methods in that it uses a nontrivial application of the calculus of differential forms. Especially, a new result on the decomposition of 1-forms is derived.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1057637
zbMATH Keywords: period coefficients
zbMATH Keywords: period functions
zbMATH Keywords: differential forms
zbMATH Keywords: Poincaré return map
author: Jean-Pierre Francoise
reviewed by: C. Chicone
MaRDI profile type: Publication
OpenAlex ID: W4232368046
description: scientific article; zbMATH DE number 1057637