58 citations · 490 across the 38 of their papers we have counts for
5 papers · 1 filter
Bifurcations in the Space of Exponential Maps
Lasse Rempe, Dierk Schleicher
This article investigates the parameter space of the exponential family . We prove that the boundary (in $\C$) of every hyperbolic component is a Jordan arc, as…
Classification of Escaping Exponential Maps
Markus Förster, Lasse Rempe, Dierk Schleicher
We give a complete classification of the set of parameters for which the singular value of escapes to infinity under iteration. In particular, we show…
Topological Dynamics of Exponential Maps on their Escaping Sets
Lasse Rempe
We develop an abstract model for the dynamics of an exponential map on its set of escaping points and, as an analog of Boettcher's theorem for polynomials, sho…
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…
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…