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

  • Identification data

    Identifier: imarina:9380947
    Authors:
    Fontich, ErnestGarijo, AntonioJarque, Xavier
    Abstract:
    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.
  • Others:

    Author, as appears in the article.: Fontich, Ernest; Garijo, Antonio; Jarque, Xavier
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Garijo Real, Antonio
    Keywords: Symbolic dynamic Stable and unstable manifold Secant map Periodic points Homoclinic connection Basin of attraction
    Abstract: 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.
    Thematic Areas: Physics, mathematical Modeling and simulation Mechanics Mathematics, applied Matemática / probabilidade e estatística General engineering Engineering (miscellaneous) Engineering (all) Applied mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: antonio.garijo@urv.cat
    Author identifier: 0000-0002-1503-7514
    Record's date: 2024-09-28
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://link.springer.com/article/10.1007/s00332-024-10079-7
    Papper original source: Journal Of Nonlinear Science. 34 (6): 102-
    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
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.1007/s00332-024-10079-7
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2024
    Publication Type: Journal Publications
  • Keywords:

    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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