Speaker
Dan Paraschiv
(IMFM Ljubljana)
Description
We study the family of Chevushev-Halley family of numerical methods, previously introduced and studied by Campos, Canela, and Vindel. We prove the existence of parameters for which all Fatou components are infinitely connected, while components of the Julia sets are quasiconformal deformations of the Newton-type Julia set.The family $\lambda z^n e^z$ for $n \ge 2$, has previously been studied by Fagella, Garijo, Jarque, Morena, etc. They investigated capture components in the parameter plane (that is, when the free critical point is attracted to the super attracting fixed point $z = 0$). Using recent advances in theory of dynamical rays we investigate the dynamics in the main Mandelbrot-like set of the parameter plane.
Author
Dan Paraschiv
(IMFM Ljubljana)
