Study of the period function of a two-parameter family of centers
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rojas, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2017
Abstract:	In this paper we study the period function of ẍ = (1 x) p − (1 x) q , with p, q ∈ R and p > q. We prove three independent results. The first one establishes some regions in the parameter space where the corresponding center has a monotonous period function. This result extends the previous ones by Miyamoto and Yagasaki for the case q = 1. The second one deals with the bifurcation of critical periodic orbits from the center. The third one is addressed to the critical periodic orbits that bifurcate from the period annulus of each one of the three isochronous centers in the family when perturbed by means of a one-parameter deformation. These three results, together with the ones that we obtained previously on the issue, leads us to propose a conjectural bifurcation diagram for the global behaviour of the period function of the family.
Grants:	Ministerio de Educación y Ciencia MTM2014-52209-C2-1-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bifurcation ; Center ; Critical periodic orbit ; Criticality ; Period function
Published in:	Journal of mathematical analysis and applications, Vol. 452 (2017) , p. 188-208, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2017.02.054

Postprint 19 p, 504.7 KB

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