Articles producció científica> Enginyeria Informàtica i Matemàtiques

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

  • Identification data

    Identifier: imarina:9282647
    Handle: https://hdl.handle.net/20.500.11797/imarina9282647
    Authors:
    Mañosas FRojas DVilladelprat J
    Abstract:
    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.

  • Others:

    Author, as appears in the article.: Mañosas F; 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: 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.
    Thematic Areas: Mathematics, applied Mathematics Matemática / probabilidade e estatística Interdisciplinar Engenharias iv Engenharias iii Ciências ambientais 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: 2023-02-19
    Papper version: info:eu-repo/semantics/acceptedVersion
    Link to the original source: https://www.sciencedirect.com/science/article/pii/S0022247X17302147
    Papper original source: Journal Of Mathematical Analysis And Applications. 452 (1): 188-208
    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
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.1016/j.jmaa.2017.02.054
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2017
    Publication Type: Journal Publications

  • Keywords:

    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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