Author, as appears in the article.: Gardini, Laura; Garijo, Antonio; Jarque, Xavier;
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Garijo Real, Antonio
Project code: PID2020-118281GB-C33
Keywords: Denominator Periodic orbits Plane maps Rational iteration Root finding algorithms Secant method
Abstract: We study the discrete dynamical system defined on a subset of R-2 given by the iterates of the secant method applied to a real polynomial p. Each simple real root a of p has associated its basin of attraction A(alpha) formed by the set of points converging towards the fixed point (alpha, alpha) of S. We denote by A* (alpha) its immediate basin of attraction, that is, the connected component of A( a) which contains (alpha, alpha). We focus on some topological properties of A* (alpha), when a is an internal real root of p. More precisely, we show the existence of a 4-cycle in. A* (alpha) and we give conditions on p to guarantee the simple connectivity of A* (alpha).
Thematic Areas: Engenharias iv Ensino General mathematics Matemática / probabilidade e estatística Mathematics Mathematics (all) Mathematics (miscellaneous) Mathematics, applied
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: 2024-07-27
Papper version: info:eu-repo/semantics/publishedVersion
Funding program: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
Papper original source: Mediterranean Journal Of Mathematics. 18 (5):
APA: Gardini, Laura; Garijo, Antonio; Jarque, Xavier; (2021). Topological Properties of the Immediate Basins of Attraction for the Secant Method. Mediterranean Journal Of Mathematics, 18(5), -. DOI: 10.1007/s00009-021-01845-y
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Acronym: ATBiD
Entity: Universitat Rovira i Virgili
Journal publication year: 2021
Funding program action: Proyectos I+D Generación de Conocimiento
Publication Type: Journal Publications
Repositori URV