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Study of the period function of a two-parameter family of centers

  • Datos identificativos

    Identificador: imarina:9282647
    Autores:
    Mañosas FRojas DVilladelprat J
    Resumen:
    In this paper we study the period function of x¨=(1+x)p?(1+x)q, with p,q?R and p>q. We prove three independent results. The first one establishes some regions in the parameter space where the corresponding center has a monotonous period function. This result extends the previous ones by Miyamoto and Yagasaki for the case q=1. The second one deals with the bifurcation of critical periodic orbits from the center. The third one is addressed to the critical periodic orbits that bifurcate from the period annulus of each one of the three isochronous centers in the family when perturbed by means of a one-parameter deformation. These three results, together with the ones that we obtained previously on the issue, lead us to propose a conjectural bifurcation diagram for the global behaviour of the period function of the family. © 2017 Elsevier Inc.
  • Otros:

    Autor según el artículo: Mañosas F; 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: In this paper we study the period function of x¨=(1+x)p?(1+x)q, with p,q?R and p>q. We prove three independent results. The first one establishes some regions in the parameter space where the corresponding center has a monotonous period function. This result extends the previous ones by Miyamoto and Yagasaki for the case q=1. The second one deals with the bifurcation of critical periodic orbits from the center. The third one is addressed to the critical periodic orbits that bifurcate from the period annulus of each one of the three isochronous centers in the family when perturbed by means of a one-parameter deformation. These three results, together with the ones that we obtained previously on the issue, lead us to propose a conjectural bifurcation diagram for the global behaviour of the period function of the family. © 2017 Elsevier Inc.
    Áreas temáticas: Mathematics, applied Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iv Engenharias iii Ciências ambientais 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: 2023-02-19
    Versión del articulo depositado: info:eu-repo/semantics/acceptedVersion
    Enlace a la fuente original: https://www.sciencedirect.com/science/article/pii/S0022247X17302147
    Referencia al articulo segun fuente origial: Journal Of Mathematical Analysis And Applications. 452 (1): 188-208
    Referencia de l'ítem segons les normes APA: Mañosas F; Rojas D; Villadelprat J (2017). Study of the period function of a two-parameter family of centers. Journal Of Mathematical Analysis And Applications, 452(1), 188-208. DOI: 10.1016/j.jmaa.2017.02.054
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI del artículo: 10.1016/j.jmaa.2017.02.054
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2017
    Tipo de publicación: Journal Publications
  • Palabras clave:

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