Fitxers
Tipus de document
ArticleVersió
Versió publicadaData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/189388
Topological properties of the immediate basins of attraction for the secant method
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
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 $\alpha$ of $p$ has associated its basin of attraction $\mathcal{A}(\alpha)$ formed by the set of points converging towards the fixed point $(\alpha, \alpha)$ of $S$. We denote by $\mathcal{A}^*(\alpha)$ its immediate basin of attraction, that is, the connected component of $\mathcal{A}(\alpha)$ which contains $(\alpha, \alpha)$. We focus on some topological properties of $\mathcal{A}^*(\alpha)$, when $\alpha$ is an internal real root of $p$. More precisely, we show the existence of a 4-cycle in $\partial \mathcal{A}^*(\alpha)$ and we give conditions on $p$ to guarantee the simple connectivity of $\mathcal{A}^*(\alpha)$.
Matèries (anglès)
Citació
Citació
GARDINI, Laura, GARIJO, Antonio and JARQUE I RIBERA, Xavier. Topological properties of the immediate basins of attraction for the secant method. Mediterranean Journal of Mathematics. 2021. Vol. 18, num. 221. ISSN 1660-5446. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/189388