Author, as appears in the article.: Fontich, Ernest; Garijo, Antonio; Jarque, Xavier
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Garijo Real, Antonio
Project code: PID2020-118281GB-C33
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
Funding program: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
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/
Acronym: ATBiD
Article's DOI: 10.1007/s00332-024-10079-7
Entity: Universitat Rovira i Virgili
Journal publication year: 2024
Funding program action: Proyectos I+D Generación de Conocimiento
Publication Type: Journal Publications
Repositori URV