Dierk Schleicher

most citedParameter rays for the exponential family

7 citations · 7 across the 1 of their papers we have counts for

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math.DS2005★ 7 cited

Parameter rays for the exponential family

Markus Förster, Dierk Schleicher

We investigate the set of parameters $κ\in\C$ for which the singular orbit $(0, e^{κ}, ...)$ of $E_{κ} (z) := exp (z + κ)$ converges to $\infty$ . These parameters are organized in smooth curv…

math.DS2004★ 9 cited

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 $W$ has connected boundary, and there is a conformal isomorp…

math.DS2004

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…