Home > Articles > Published articles > New lower bounds of the number of critical periods in reversible centers |
Date: | 2021 |
Abstract: | In this paper we aim to find the highest number of critical periods in a class of planar systems of polynomial differential equations for fixed degree having a center. We fix our attention to lower bounds of local criticality for low degree planar polynomial centers. The main technique is the study of perturbations of reversible holomorphic (isochronous) centers, inside the reversible centers class. More concretely, we study the Taylor developments of the period constants with respect to the perturbation parameters. First, we see that there are systems of degree 3≤n≤16 for which up to first order at least (n+n−4)/2 critical periods bifurcate from the center. Second, we improve this number for centers with degree from 3 to 9. In particular, we obtain 6 and 10 critical periods for cubic and quartic degree systems, respectively. |
Grants: | Agencia Estatal de Investigación PID2019-104658GB-I00 Ministerio de Educación, Cultura y Deporte FPU16/04317 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 |
Rights: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Bifurcation of critical periods ; Criticality ; Period constants ; Period function ; Time-reversible centers |
Published in: | Journal of differential equations, Vol. 292 (August 2021) , p. 427-460, ISSN 1090-2732 |
Postprint 29 p, 980.9 KB |