Articles producció científica> Enginyeria Informàtica i Matemàtiques

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

  • Identification data

    Identifier: imarina:5131974
  • Authors:

    Rojas, D.
    Villadelprat, J.
  • Others:

    Author, as appears in the article.: Rojas, D.; Villadelprat, J.;
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Villadelprat Yagüe, Jordi
    Keywords: Period function Criticality Critical periodic orbit Center Bifurcation
    Abstract: © 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.
    Thematic Areas: Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iii Ciências agrárias i Ciência da computação Astronomia / física Applied mathematics Analysis
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: jordi.villadelprat@urv.cat
    Author identifier: 0000-0002-1168-9750
    Record's date: 2023-02-18
    Papper version: info:eu-repo/semantics/acceptedVersion
    Link to the original source: https://www.sciencedirect.com/science/article/abs/pii/S0022039618300597
    Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Journal Of Differential Equations. 264 (11): 6585-6602
    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
    Article's DOI: 10.1016/j.jde.2018.01.042
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2018
    Publication Type: Journal Publications
  • Keywords:

    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
  • Documents:

  • Cerca a google

    Search to google scholar