Lasse Rempe

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20032008

most citedOn a question of Eremenko concerning escaping components of entire functions

28 citations · 54 across the 3 of their papers we have counts for

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Showing 2003 · math.DSShow all

5 papers · 2 filters

math.DS2003

Bifurcations in the Space of Exponential Maps

Lasse Rempe, Dierk Schleicher

This article investigates the parameter space of the exponential family $z \mapsto exp (z) + κ$ . We prove that the boundary (in $\C$) of every hyperbolic component is a Jordan arc, as…

math.DS2003

Classification of Escaping Exponential Maps

Markus Förster, Lasse Rempe, Dierk Schleicher

We give a complete classification of the set of parameters $κ$ for which the singular value of $E_{κ} : z \mapsto exp (z) + κ$ escapes to infinity under iteration. In particular, we show…

math.DS2003

Topological Dynamics of Exponential Maps on their Escaping Sets

Lasse Rempe

We develop an abstract model for the dynamics of an exponential map $z \mapsto exp (z) + κ$ on its set of escaping points and, as an analog of Boettcher's theorem for polynomials, sho…

math.DS2003

An answer to a question of Herman, Baker and Rippon concerning Siegel disks

Lasse Rempe

We give a positive answer to a question of Herman, Baker and Rippon by showing that, in the exponential family, the boundary of every unbounded Siegel disk contains the singular va…

math.DS2003

A Landing Theorem for Periodic Rays of Exponential Maps

Lasse Rempe

We answer a question of Schleicher by showing that, for an exponential map with nonescaping singular value, every periodic ray lands. This is an analog of a theorem of Douady and H…