4 papers · 1 filter
Achievable connectivities of Fatou components for a family of singular perturbations
Jordi Canela, Xavier Jarque, Dan Paraschiv
In this paper we study the connectivity of Fatou components for maps in a large family of singular perturbations. We prove that, for some parameters inside the family, the dynamica…
Topological properties of the immediate basins of attraction for the secant method
Laura Gardini, Antonio Garijo, Xavier Jarque
We study the discrete dynamical system defined on a subset of given by the iterates of the secant method applied to a real polynomial . Each simple real root of ha…
The secant map applied to a real polynomial with multiple roots
Antonio Garijo, Xavier Jarque
We investigate the plane dynamical system given by the secant map applied to a polynomial having at least one multiple root of multiplicity . We prove that the local dynam…
Global dynamics of the real secant method
Antonio Garijo, Xavier Jarque
We investigate the root finding algorithm given by the secant method applied to a real polynomial as a discrete dynamical system defined on . We study the shape an…