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| Pàgina inicial > Articles > Articles publicats > Global behaviour of the period function for some degenerate centers |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)| Data: | 2017 |
| Resum: | 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. |
| Ajuts: | 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 |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Center ; Critical period ; Degenerate critical point ; Hamiltonian system ; Period function |
| Publicat a: | Journal of mathematical analysis and applications, Vol. 449 Núm. 2 (2017) , p. 1553-1569, ISSN 1096-0813 |
18 p, 330.6 KB |
