17 citations · 69 across the 12 of their papers we have counts for
21 papers
On a result of Hayman concerning the maximum modulus set
Vasiliki Evdoridou, Leticia Pardo-Simón, David J. Sixsmith
The set of points where an entire function achieves its maximum modulus is known as the maximum modulus set. In 1951, Hayman studied the structure of this set near the origin. Foll…
The maximum modulus set of a quasiregular map
Alastair N. Fletcher, David J. Sixsmith
We study, for the first time, the maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point of each modulu…
Geometrically finite transcendental entire functions
Mashael Alhamed, Lasse Rempe, Dave Sixsmith
For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, when the Julia set of a polynomial of degree is locally connected, the…
Fatou's associates
Vasiliki Evdoridou, Lasse Rempe, David J. Sixsmith
Suppose that is a transcendental entire function, is a simply connected domain, and is a connected component of . Using Riemann maps, w…
On the connectivity of the escaping set in the punctured plane
Vasiliki Evdoridou, David Martí-Pete, David J. Sixsmith
We consider the dynamics of transcendental self-maps of the punctured plane, . We prove that the escaping set is either connected, or…
Which sequences are orbits?
Daniel A. Nicks, David J. Sixsmith
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the func…