Global behaviour of the period function of the sum of two quasi-homogeneous vector fields
type: Item
instance of: scholarly article
title: Global behaviour of the period function of the sum of two quasi-homogeneous vector fields
zbMATH Open document ID: 1369.34046
author: Armengol Gasull
author: M. J. Álvarez
author: Rafel Prohens
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-02-08T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/182499
review text: In this paper, the authors study the global behaviour of the period function on the period annulus of degenerate centres for two families of planar polynomial vector fields. These families are the quasi-homogeneous vector fields and the vector fields given by the sum of two quasi-homogeneous Hamiltonian ones. For the first family, it is proved that the period function is globally decreasing, extending previous results that deal either with the Hamiltonian quasi-homogeneous case or with the general homogeneous situation. For the second family, after adding some more additional hypotheses, it is shown that the period function of the origin is either decreasing or has at most one critical period and that both possibilities may happen. The authors also extend some previous results that deal with the situation where both vector fields are homogeneous and the origin is a non-degenerate centre.
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6682110
zbMATH Keywords: planar polynomial vector field
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: centre
zbMATH Keywords: period function
zbMATH Keywords: critical period
zbMATH Keywords: degenerate critical point
MaRDI profile type: Publication
OpenAlex ID: W2571461823
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DOI: 10.1016/J.JMAA.2016.12.077
description: scientific article; zbMATH DE number 6682110