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

  • Datos identificativos

    Identificador: imarina:9380947
    Autores:
    Fontich, ErnestGarijo, AntonioJarque, Xavier
    Resumen:
    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.
  • Otros:

    Autor según el artículo: Fontich, Ernest; Garijo, Antonio; Jarque, Xavier
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Garijo Real, Antonio
    Código de proyecto: PID2020-118281GB-C33
    Palabras clave: Symbolic dynamic Stable and unstable manifold Secant map Periodic points Homoclinic connection Basin of attraction
    Resumen: 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.
    Áreas temáticas: Physics, mathematical Modeling and simulation Mechanics Mathematics, applied Matemática / probabilidade e estatística General engineering Engineering (miscellaneous) Engineering (all) Applied mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: antonio.garijo@urv.cat
    Identificador del autor: 0000-0002-1503-7514
    Fecha de alta del registro: 2024-09-28
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://link.springer.com/article/10.1007/s00332-024-10079-7
    Programa de financiación: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Referencia al articulo segun fuente origial: Journal Of Nonlinear Science. 34 (6): 102-
    Referencia 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 Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrónimo: ATBiD
    DOI del artículo: 10.1007/s00332-024-10079-7
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2024
    Acción del progama de financiación: Proyectos I+D Generación de Conocimiento
    Tipo de publicación: Journal Publications
  • Palabras clave:

    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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