30 citations · 87 across the 6 of their papers we have counts for
13 papers
Eventual hyperbolic dimension of entire functions and Poincaré functions of polynomials
Alexandre DeZotti, Lasse Rempe-Gillen
Let be an entire function. A Poincaré function of is the entire extension of a linearising coord…
On connected preimages of simply-connected domains under entire functions
Lasse Rempe-Gillen, Dave Sixsmith
Let be a transcendental entire function, and let be disjoint simply-connected domains. Must one of and be disconnected? In 1970,…
Non-escaping endpoints do not explode
Vasiliki Evdoridou, Lasse Rempe-Gillen
The family of exponential maps is of fundamental importance in the study of transcendental dynamics. Here we consider the topological structure of certain subsets o…
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…
Escaping endpoints explode
Nada Alhabib, Lasse Rempe-Gillen
In 1988, Mayer proved the remarkable fact that infinity is an explosion point for the set of endpoints of the Julia set of an exponential map that has an attracting fixed point. Th…
Hyperbolic entire functions and the Eremenko-Lyubich class: Class or not class ?
Lasse Rempe-Gillen, Dave Sixsmith
Hyperbolicity plays an important role in the study of dynamical systems, and is a key concept in the iteration of rational functions of one complex variable. Hyperbolic systems hav…