7 papers
Arc-like continua, Julia sets of entire functions, and Eremenko's Conjecture
Lasse Rempe
A hyperbolic transcendental entire function with connected Fatou set is said to be "of disjoint type". It is known that a disjoint-type function provides a model for the dynamics n…
Wandering dynamics of transcendental functions
Vasiliki Evdoridou, David MartÃ-Pete, Lasse Rempe
We show that any uniformly escaping and wandering dynamics of a holomorphic function on a compact subset of the plane can be realised by a transcendental meromorphic function on $\…
Non-compact Riemann surfaces are equilaterally triangulable
Christopher J. Bishop, Lasse Rempe
We show that every open Riemann surface can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely man…
The escaping set in transcendental dynamics
Walter Bergweiler, Lasse Rempe
The escaping set of an entire function consists of the points in the complex plane that tend to infinity under iteration. This set plays a central role in the dynamics of transcend…
Entire functions with Cantor bouquet Julia sets
Leticia Pardo-Simón, Lasse Rempe
A hyperbolic transcendental entire function with connected Fatou set is said to be of disjoint type. It is known that the Julia set of a disjoint-type function of finite order is a…
Spiders' webs in the Eremenko-Lyubich class
Lasse Rempe
Consider the entire function . We show that the escaping set of this function - that is, the set of points whose orbits tend to infinity under iteration - has a stru…