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DC Field | Value | Language |
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dc.contributor.author | Gardini, Laura | - |
dc.contributor.author | Garijo, Antonio | - |
dc.contributor.author | Jarque i Ribera, Xavier | - |
dc.date.accessioned | 2022-09-28T08:12:18Z | - |
dc.date.available | 2022-09-28T08:12:18Z | - |
dc.date.issued | 2021-09-07 | - |
dc.identifier.issn | 1660-5446 | - |
dc.identifier.uri | http://hdl.handle.net/2445/189388 | - |
dc.description.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 $\alpha$ 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 $\mathcal{A}^*(\alpha)$. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1007/s00009-021-01845-y | - |
dc.relation.ispartof | Mediterranean Journal of Mathematics, 2021, vol. 18, num. 221 | - |
dc.relation.uri | https://doi.org/10.1007/s00009-021-01845-y | - |
dc.rights | cc by (c) Laura Gardini et al., 2021 | - |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Teoria de la bifurcació | - |
dc.subject.classification | Sistemes dinàmics diferenciables | - |
dc.subject.classification | Anàlisi numèrica | - |
dc.subject.other | Bifurcation theory | - |
dc.subject.other | Differentiable dynamical systems | - |
dc.subject.other | Numerical analysis | - |
dc.title | Topological properties of the immediate basins of attraction for the secant method | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.type | info:eu-repo/semantics/article | - |
dc.identifier.idgrec | 725145 | - |
dc.date.updated | 2022-09-28T08:12:18Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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725145.pdf | 2.63 MB | Adobe PDF | View/Open |
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