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 $d$.

Bibliographic Details
Authors: Garijo Real, Antonio, Jarque i Ribera, Xavier
Format: article
Status:Versión aceptada para publicación
Publication Date:2020
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/200327
Online Access:https://hdl.handle.net/2445/200327
Access Level:Open access
Keyword:Teoria de la bifurcació
Sistemes dinàmics diferenciables
Bifurcation theory
Differentiable dynamical systems
Description
Summary: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 $d$.