dc.contributor.author |
Gardini, Laura |
dc.contributor.author |
Garijo, Antoni |
dc.contributor.author |
Jarque i Ribera, Xavier |
dc.date |
2021 |
dc.date.accessioned |
2022-10-31T18:28:37Z |
dc.date.available |
2022-10-31T18:28:37Z |
dc.date.issued |
2022-10-31 |
dc.identifier |
https://ddd.uab.cat/record/257106 |
dc.identifier |
urn:10.1007/s00009-021-01845-y |
dc.identifier |
urn:oai:ddd.uab.cat:257106 |
dc.identifier |
urn:scopus_id:85114391646 |
dc.identifier |
urn:articleid:16605454v18n5p221 |
dc.identifier |
urn:gsduab:5021 |
dc.identifier.uri |
http://hdl.handle.net/2072/527180 |
dc.format |
application/pdf |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Agencia Estatal de Investigación MTM-2017-86795-C3-2-P |
dc.relation |
Agencia Estatal de Investigación MTM-2017-86795-C3-3-P |
dc.relation |
Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374 |
dc.relation |
Mediterranean Journal of Mathematics ; Vol. 18, Issue 5 (October 2021), art. 221 |
dc.rights |
open access |
dc.rights |
Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original. |
dc.rights |
https://creativecommons.org/licenses/by/4.0/ |
dc.subject |
Root finding algorithms |
dc.subject |
Rational iteration |
dc.subject |
Secant method |
dc.subject |
Periodic orbits |
dc.title |
Topological properties of the immediate basins of attraction for the secant method |
dc.type |
Article |
dc.description.abstract |
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). |