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A criticality result for polycycles in a family of quadratic reversible centers

  • Dades identificatives

    Identificador: imarina:5131974
    Autors:
    Rojas, D.Villadelprat, J.
    Resum:
    © 2018 Elsevier Inc. We consider the family of dehomogenized Loud's centers Xμ=y(x−1)∂x+(x+Dx2+Fy2)∂y, where μ=(D,F)∈R2, and we study the number of critical periodic orbits that emerge or disappear 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∈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.
  • Altres:

    Autor segons l'article: Rojas, D.; Villadelprat, J.;
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Villadelprat Yagüe, Jordi
    Paraules clau: Period function Criticality Critical periodic orbit Center Bifurcation
    Resum: © 2018 Elsevier Inc. We consider the family of dehomogenized Loud's centers Xμ=y(x−1)∂x+(x+Dx2+Fy2)∂y, where μ=(D,F)∈R2, and we study the number of critical periodic orbits that emerge or disappear 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∈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.
    Àrees temàtiques: Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iii Ciências agrárias i Ciência da computação Astronomia / física Applied mathematics Analysis
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: jordi.villadelprat@urv.cat
    Identificador de l'autor: 0000-0002-1168-9750
    Data d'alta del registre: 2023-02-18
    Versió de l'article dipositat: info:eu-repo/semantics/acceptedVersion
    Enllaç font original: https://www.sciencedirect.com/science/article/abs/pii/S0022039618300597
    Referència a l'article segons font original: Journal Of Differential Equations. 264 (11): 6585-6602
    Referència de l'ítem segons les normes APA: Rojas, D.; Villadelprat, J.; (2018). A criticality result for polycycles in a family of quadratic reversible centers. Journal Of Differential Equations, 264(11), 6585-6602. DOI: 10.1016/j.jde.2018.01.042
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI de l'article: 10.1016/j.jde.2018.01.042
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2018
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Analysis,Applied Mathematics,Mathematics
    Period function
    Criticality
    Critical periodic orbit
    Center
    Bifurcation
    Mathematics
    Matemática / probabilidade e estatística
    Interdisciplinar
    Engenharias iii
    Ciências agrárias i
    Ciência da computação
    Astronomia / física
    Applied mathematics
    Analysis
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