8 citations · 17 across the 8 of their papers we have counts for
10 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…
Transcendental correspondences: when Fuchsian groups take over basins of entire maps
Kostiantyn Drach, Sabyasachi Mukherjee, Leticia Pardo-Simón
In this paper, we initiate a systematic study of holomorphic correspondences that naturally arise as conformal combinations (matings) of transcendental entire m…
On the dimension of the boundaries of attracting basins of entire maps
Krzysztof Barański, Bogusława Karpińska, David Martí-Pete +2
Let be a transcendental entire map from the Eremenko-Lyubich class , and let be an attracting periodic point of period . We…
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…
An approximate solution to Erdös' maximum modulus points problem
Adi Glücksam, Leticia Pardo-Simón
In this note we investigate the asymptotic behavior of the number of maximum modulus points, of an entire function, sitting in a disc of radius . In 1964, Erd\Humlaut{o}s asked…
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…
Combinatorics of criniferous entire maps with escaping critical values
Leticia Pardo-Simón
A transcendental entire function is called criniferous if every point in its escaping set can eventually be connected to infinity by a curve of escaping points. Many transcendental…
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…
Orbifold expansion and entire functions with bounded Fatou components
Leticia Pardo-Simón
Many authors have studied the dynamics of hyperbolic transcendental entire functions; these are those for which the postsingular set is a compact subset of the Fatou set. Equivalen…