Topological properties of the immediate basins of attraction for the secant method
We study the discrete dynamical system defined on a subset of R given by the iterates of the secant method applied to a real polynomial p. Each simple real root α of p has associated its basin of attraction A(α) formed by the set of points converging towards the fixed point (α, α) of S. We denote by...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:257106 |
| Acceso en línea: | https://ddd.uab.cat/record/257106 https://dx.doi.org/urn:doi:10.1007/s00009-021-01845-y |
| Access Level: | acceso abierto |
| Palabra clave: | Root finding algorithms Rational iteration Secant method Periodic orbits |
| Sumario: | We study the discrete dynamical system defined on a subset of R given by the iterates of the secant method applied to a real polynomial p. Each simple real root α of p has associated its basin of attraction A(α) formed by the set of points converging towards the fixed point (α, α) of S. We denote by A(α) its immediate basin of attraction, that is, the connected component of A(α) which contains (α, α). We focus on some topological properties of A(α), when α is an internal real root of p. More precisely, we show the existence of a 4-cycle in ∂A(α) and we give conditions on p to guarantee the simple connectivity of A(α). |
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