9 citations · 16 across the 3 of their papers we have counts for
5 papers · 1 filter
Parameter rays for the exponential family
Markus Förster, Dierk Schleicher
We investigate the set of parameters $κ\in\C$ for which the singular orbit of converges to . These parameters are organized in smooth curv…
Hyperbolic Components in Exponential Parameter Space
Dierk Schleicher
We discuss the space of complex exponential maps $\Ek\colon z\mapsto e^{z}+κ$. We prove that every hyperbolic component has connected boundary, and there is a conformal isomorp…
Immediate and Virtual Basins of Newton's Method for Entire Functions
Sebastian Mayer, Dierk Schleicher
We investigate the well known Newton method to find roots of entire holomorphic functions. Our main result is that the immediate basin of attraction for every root is simply connec…
On Fibers and Renormalization of Julia Sets and Multibrot Sets
Dierk Schleicher
We continue the description of Mandelbrot and Multibrot sets and of Julia sets in terms of fibers which was begun in IMS preprints 1998/12 and 1998/13a. The question of local conne…
On Fibers and Local Connectivity of Compact Sets in C
Dierk Schleicher
A frequent problem in holomorphic dynamics is to prove local connectivity of Julia sets and of many points of the Mandelbrot set; local connectivity has many interesting implicatio…