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Global behaviour of the period function for some degenerate centers
Álvarez, Maria Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)

Date: 2017
Abstract: We study the global behaviour of the period function on the period annulus of degenerate centers 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. In the first case we prove 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. In the second family, and after adding some more additional hypotheses, we show that the period function of the origin is either decreasing or has at most one critical period and that both possibilities may happen. This result also extends some previous results that deal with the situation where both vector fields are homogenous and the origin is a non-degenerate center.
Grants: Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
European Commission 318999
Ministerio de Economía y Competitividad MTM2014-54275-P
Ministerio de Economía y Competitividad MTM2011-22751
Ministerio de Economía y Competitividad MTM2013-40998-P
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Subject: Center ; Critical period ; Degenerate critical point ; Hamiltonian system ; Period function
Published in: Journal of mathematical analysis and applications, Vol. 449 Núm. 2 (2017) , p. 1553-1569, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2016.12.077


Postprint
18 p, 330.6 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2017-11-28, last modified 2022-09-16



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