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
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
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Article's DOI: 10.1016/j.jde.2018.01.042
Entity: Universitat Rovira i Virgili
Journal publication year: 2018
Publication Type: Journal Publications
Repositori URV