4 papers
Wiman-Valiron discs and the dimension of Julia sets
James Waterman
We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on t…
Identifying logarithmic tracts
James Waterman
We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an applicat…
Slow escape in tracts
James Waterman
Let be a transcendental entire function. By a result of Rippon and Stallard, there exist points whose orbit escapes arbitrarily slowly. By using a range of techniques to prove…
On the infinitesimal space of uqr mappings
Alastair Fletcher, Doug Macclure, James Waterman +1
Generalized derivatives and infinitesimal spaces generalize the idea of derivatives to mappings which need not be differentiable. It is particularly powerful in the context of quas…