Criticality via first order development of the period constants
Sánchez-Sánchez, Iván (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	In this work we study the criticality of some planar systems of polynomial differential equations having a center for various low degrees n. To this end, we present a method which is equivalent to the use of the first non-identically zero Melnikov function in the problem of limit cycles bifurcation, but adapted to the period function. We prove that the Taylor development of this first order function can be found from the linear terms of the corresponding period constants. Later, we consider families which are isochronous centers being perturbed inside the reversible centers class, and we prove our criticality results by finding the first order Taylor developments of the period constants with respect to the perturbation parameters. In particular, we obtain that at least 22 critical periods bifurcate for n = 6, 37 for n = 8, 57 for n = 10, 80 for n = 12, 106 for n = 14, and 136 for n = 16. Up to our knowledge, these values improve the best current lower bounds.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad PID2019-104658GB-I00 Ministerio de Economía y Competitividad 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:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 203 (February 2021) , art. 112164, ISSN 0362-546X

DOI: 10.1016/j.na.2020.112164

Postprint 22 p, 352.2 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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