The secant applied to a real polynomial with multiple roots

We investigate the plane dynamical system given by the secant map applied to a polynomial $p$ having at least one multiple root of multiplicity $d>1$. We prove that the local dynamics around the fixed points related to the roots of $p$ depend on the parity of $d$.

Detalhes bibliográficos
Autores: Garijo Real, Antonio, Jarque i Ribera, Xavier
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2020
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositório:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/200327
Acesso em linha:https://hdl.handle.net/2445/200327
Access Level:Acceso aberto
Palavra-chave:Teoria de la bifurcació
Sistemes dinàmics diferenciables
Bifurcation theory
Differentiable dynamical systems
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spelling The secant applied to a real polynomial with multiple rootsGarijo Real, AntonioJarque i Ribera, XavierTeoria de la bifurcacióSistemes dinàmics diferenciablesBifurcation theoryDifferentiable dynamical systemsWe investigate the plane dynamical system given by the secant map applied to a polynomial $p$ having at least one multiple root of multiplicity $d>1$. We prove that the local dynamics around the fixed points related to the roots of $p$ depend on the parity of $d$.American Institute of Mathematical Sciences (AIMS)2023202320202023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion12 p.application/pdfhttps://hdl.handle.net/2445/200327Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.3934/dcds.2020133Discrete and Continuous Dynamical Systems-Series A, 2020, vol. 40, num. 12, p. 6783-6794https://doi.org/10.3934/dcds.2020133(c) American Institute of Mathematical Sciences (AIMS), 2020info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2003272026-05-29T05:05:01Z
dc.title.none.fl_str_mv The secant applied to a real polynomial with multiple roots
title The secant applied to a real polynomial with multiple roots
spellingShingle The secant applied to a real polynomial with multiple roots
Garijo Real, Antonio
Teoria de la bifurcació
Sistemes dinàmics diferenciables
Bifurcation theory
Differentiable dynamical systems
title_short The secant applied to a real polynomial with multiple roots
title_full The secant applied to a real polynomial with multiple roots
title_fullStr The secant applied to a real polynomial with multiple roots
title_full_unstemmed The secant applied to a real polynomial with multiple roots
title_sort The secant applied to a real polynomial with multiple roots
dc.creator.none.fl_str_mv Garijo Real, Antonio
Jarque i Ribera, Xavier
author Garijo Real, Antonio
author_facet Garijo Real, Antonio
Jarque i Ribera, Xavier
author_role author
author2 Jarque i Ribera, Xavier
author2_role author
dc.subject.none.fl_str_mv Teoria de la bifurcació
Sistemes dinàmics diferenciables
Bifurcation theory
Differentiable dynamical systems
topic Teoria de la bifurcació
Sistemes dinàmics diferenciables
Bifurcation theory
Differentiable dynamical systems
description We investigate the plane dynamical system given by the secant map applied to a polynomial $p$ having at least one multiple root of multiplicity $d>1$. We prove that the local dynamics around the fixed points related to the roots of $p$ depend on the parity of $d$.
publishDate 2020
dc.date.none.fl_str_mv 2020
2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/200327
url https://hdl.handle.net/2445/200327
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.3934/dcds.2020133
Discrete and Continuous Dynamical Systems-Series A, 2020, vol. 40, num. 12, p. 6783-6794
https://doi.org/10.3934/dcds.2020133
dc.rights.none.fl_str_mv (c) American Institute of Mathematical Sciences (AIMS), 2020
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Institute of Mathematical Sciences (AIMS), 2020
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 12 p.
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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