Autor según el artículo: Gardini, Laura; Garijo, Antonio; Jarque, Xavier;
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Garijo Real, Antonio
Palabras clave: Secant method Root finding algorithms Rational iteration Plane maps Periodic orbits Denominator
Resumen: 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).
Áreas temáticas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ensino Engenharias iv
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: 2024-07-27
Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
Enlace a la fuente original: https://link.springer.com/article/10.1007/s00009-021-01845-y
URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Mediterranean Journal Of Mathematics. 18 (5):
Referencia de l'ítem segons les normes 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
DOI del artículo: 10.1007/s00009-021-01845-y
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2021
Tipo de publicación: Journal Publications
Repositori URV