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
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/
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2018
Tipus de publicació: Journal Publications
Repositori URV