28 citations · 54 across the 3 of their papers we have counts for
11 papers
Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyperbolicity
Lasse Rempe, Dierk Schleicher
We study the bifurcation loci of quadratic (and unicritical) polynomials and exponential maps. We outline a proof that the exponential bifurcation locus is connected; this is an an…
Hyperbolic dimension and radial Julia sets of transcendental functions
Lasse Rempe
We survey the definition of the radial Julia set of a meromorphic function (in fact, more generally, any "Ahlfors islands map"), and give a simple proof that the Hausdorff dimensio…
On a question of Eremenko concerning escaping components of entire functions
Lasse Rempe
Let f be an entire function with a bounded set of singular values, and suppose furthermore that the postsingular set of f is bounded. We show that every component of the escaping s…
On Nonlanding Dynamic Rays of Exponential Maps
Lasse Rempe
We consider the case of an exponential map for which the singular value is accessible from the set of escaping points. We show that there are dynamic rays of which do not land. In…
Siegel Disks and Periodic Rays of Entire Functions
Lasse Rempe
Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk such that f restricts to a homeomorphism of the boundary. We show that the…
Combinatorics of Bifurcations in Exponential Parameter Space
Lasse Rempe, Dierk Schleicher
We give a complete combinatorial description of the bifurcation structure in the space of exponential maps . This combinatorial structure is the basis for a numb…