24 citations · 24 across the 2 of their papers we have counts for
7 papers · 1 filter
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 $\…
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…
Eremenko's conjecture, wandering Lakes of Wada, and maverick points
David MartÃ-Pete, Lasse Rempe, James Waterman
We develop a general technique for realising full closed subsets of the complex plane as wandering sets of entire functions. Using this construction, we solve a number of open prob…