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Chaotic Dynamics at the Boundary of a Basin of Attraction via Non-transversal Intersections for a Non-global Smooth Diffeomorphism

  • Dades identificatives

    Identificador: imarina:9380947
    Autors:
    Fontich, ErnestGarijo, AntonioJarque, Xavier
    Resum:
    In this paper, we give analytic proofs of the existence of transversal homoclinic points for a family of non-globally smooth diffeomorphisms having the origin as a fixed point which come out as a truncated map governing the local dynamics near a critical period three-cycle associated with the Secant map. Using Moser's version of Birkhoff-Smale's theorem, we prove that the boundary of the basin of attraction of the origin contains a Cantor-like invariant subset such that the restricted dynamics to it is conjugate to the full shift of N-symbols for any integer N >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 2$$\end{document} or infinity.
  • Altres:

    Autor segons l'article: Fontich, Ernest; Garijo, Antonio; Jarque, Xavier
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Garijo Real, Antonio
    Codi de projecte: PID2020-118281GB-C33
    Paraules clau: Symbolic dynamic Stable and unstable manifold Secant map Periodic points Homoclinic connection Basin of attraction
    Resum: In this paper, we give analytic proofs of the existence of transversal homoclinic points for a family of non-globally smooth diffeomorphisms having the origin as a fixed point which come out as a truncated map governing the local dynamics near a critical period three-cycle associated with the Secant map. Using Moser's version of Birkhoff-Smale's theorem, we prove that the boundary of the basin of attraction of the origin contains a Cantor-like invariant subset such that the restricted dynamics to it is conjugate to the full shift of N-symbols for any integer N >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 2$$\end{document} or infinity.
    Àrees temàtiques: Physics, mathematical Modeling and simulation Mechanics Mathematics, applied Matemática / probabilidade e estatística General engineering Engineering (miscellaneous) Engineering (all) Applied mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: antonio.garijo@urv.cat
    Identificador de l'autor: 0000-0002-1503-7514
    Data d'alta del registre: 2024-09-28
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://link.springer.com/article/10.1007/s00332-024-10079-7
    Programa de finançament: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Referència a l'article segons font original: Journal Of Nonlinear Science. 34 (6): 102-
    Referència de l'ítem segons les normes APA: Fontich, Ernest; Garijo, Antonio; Jarque, Xavier (2024). Chaotic Dynamics at the Boundary of a Basin of Attraction via Non-transversal Intersections for a Non-global Smooth Diffeomorphism. Journal Of Nonlinear Science, 34(6), 102-. DOI: 10.1007/s00332-024-10079-7
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrònim: ATBiD
    DOI de l'article: 10.1007/s00332-024-10079-7
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2024
    Acció del programa de finançament: Proyectos I+D Generación de Conocimiento
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Applied Mathematics,Engineering (Miscellaneous),Mathematics, Applied,Mechanics,Modeling and Simulation,Physics, Mathematical
    Symbolic dynamic
    Stable and unstable manifold
    Secant map
    Periodic points
    Homoclinic connection
    Basin of attraction
    Physics, mathematical
    Modeling and simulation
    Mechanics
    Mathematics, applied
    Matemática / probabilidade e estatística
    General engineering
    Engineering (miscellaneous)
    Engineering (all)
    Applied mathematics
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