Gardini, LauraGarijo, AntonioJarque i Ribera, Xavier2022-09-282022-09-282021-09-071660-5446https://hdl.handle.net/2445/189388We 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 $\mathcal{A}^*(\alpha)$.application/pdfengcc by (c) Laura Gardini et al., 2021http://creativecommons.org/licenses/by/3.0/es/Teoria de la bifurcacióSistemes dinàmics diferenciablesAnàlisi numèricaBifurcation theoryDifferentiable dynamical systemsNumerical analysisinfo:eu-repo/semantics/publishedVersion7251452022-09-28info:eu-repo/semantics/openAccess