22 citations · 25 across the 3 of their papers we have counts for
6 papers
The iterated minimum modulus and conjectures of Baker and Eremenko
J. W. Osborne, P. J. Rippon, G. M. Stallard
In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take…
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…
On the set where the iterates of an entire function are neither escaping nor bounded
J. W. Osborne, D. J. Sixsmith
For a transcendental entire function f, we study the set of points BU(f) whose iterates under f neither escape to infinity nor are bounded. We give new results on the connectedness…
Connectedness properties of the set where the iterates of an entire function are bounded
John Osborne
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. In particular, we describe a class of transcendental…
Spiders' webs and locally connected Julia sets of transcendental entire functions
J. W. Osborne
We show that, if the Julia set of a transcendental entire function is locally connected, then it takes the form of a spider's web in the sense defined by Rippon and Stallard. In th…
The structure of spider's web fast escaping sets
J. W. Osborne
Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. O…