Autor según el artículo: Rojas, D.; Villadelprat, J.;
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Villadelprat Yagüe, Jordi
Palabras clave: Period function Criticality Critical periodic orbit Center Bifurcation
Resumen: © 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.
Áreas temáticas: Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iii Ciências agrárias i Ciência da computação Astronomia / física Applied mathematics Analysis
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
Direcció de correo del autor: jordi.villadelprat@urv.cat
Identificador del autor: 0000-0002-1168-9750
Fecha de alta del registro: 2023-02-18
Versión del articulo depositado: info:eu-repo/semantics/acceptedVersion
Enlace a la fuente original: https://www.sciencedirect.com/science/article/abs/pii/S0022039618300597
URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Journal Of Differential Equations. 264 (11): 6585-6602
Referencia 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
DOI del artículo: 10.1016/j.jde.2018.01.042
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2018
Tipo de publicación: Journal Publications
Repositori URV