6 citations · 14 across the 7 of their papers we have counts for
7 papers
A finite-order answer to a problem of Erdős on maximum modulus points
Leticia Pardo-Simón, David J. Sixsmith
In 1964, Erdős asked whether, for a non-monomial entire function, the number of maximum modulus points on the circle \(|z|=r\) can become arbitrarily large as . In 1968…
Wandering domains with nearly bounded orbits
Leticia Pardo-Simón, David J. Sixsmith
A major open question in transcendental dynamics asks if it is possible for points in a wandering domain to have bounded orbits, and more strongly, for a wandering domain to iterat…
The maximum modulus set of a polynomial
L. Pardo-Simón, D. J. Sixsmith
We study the maximum modulus set, , of a polynomial . We are interested in constructing so that has certain exceptional features. Jassim and…
Variations on a theme of Hardy concerning the maximum modulus
L. Pardo-Simón, D. J. Sixsmith
In 1909, Hardy gave an example of a transcendental entire function, , with the property that the set of points where achieves its maximum modulus, , has infi…
The bungee set in quasiregular dynamics
Daniel A. Nicks, David J. Sixsmith
In complex dynamics, the bungee set is defined as the set points whose orbit is neither bounded nor tends to infinity. In this paper we study, for the first time, the bungee set of…
On permutable meromorphic functions
J. W. Osborne, D. J. Sixsmith
We study the class of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in , with at least one…