A criticality result for polycycles in a family of quadratic reversible centers
Rojas, David (Universidad de Granada. Departamento de Matemática Aplicada)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2018
Abstract:	We consider the family of dehomogenized Loud's centers Xµ_=y(x-1)∂ₓ + (x + Dx² + Fy²)_y, where µ=(D,F)єR², and we study the number of critical periodic orbits that emerge or dissapear from the polycycle at the boundary of the period annulus. This number is defined exactly the same way as the well-known notion of cyclicity of a limit periodic set and we call it criticality. The previous results on the issue for the family {Xµ,µ є R²} distinguish between parameters with criticality equal to zero (regular parameters) and those with criticality greater than zero (bifurcation parameters). A challenging problem not tackled so far is the computation of the criticality of the bifurcation parameters, which form a set ΓB of codimension 1 in R². In the present paper we succeed in proving that a subset of ΓB has criticality equal to one.
Grants:	Ministerio de Economía y Competitividad 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 ; Ceriod function
Published in:	Journal of differential equations, Vol. 264, issue 11 (June 2018) , p. 6585-6602, ISSN 1090-2732

DOI: 10.1016/j.jde.2018.01.042

Postprint 15 p, 468.0 KB

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