5 citations · 7 across the 11 of their papers we have counts for
7 papers · 1 filter
On the Modulus of a Union of Nested Annuli
Mark Comerford
We prove a result which gives sufficient conditions for a conformal annulus which is a countable union of nested conformal annuli to have bounded modulus. Our theorem also gives es…
Preservation of External Rays in non-Autonomous Iteration
Mark Comerford, Todd Woodard
We consider the dynamics arising from the iteration of an arbitrary sequence of polynomials with uniformly bounded degrees and coefficients and show that, as parameters vary within…
A Straightening Theorem for non-Autonomous Iteration
Mark Comerford
The classical straightening theorem as proved by Douady and Hubbard shows that a polynomial-like sequence is hybrid equivalent to a polynomial. We generalize this result to non-aut…
Non-Autonomous Julia Sets with Invariant Sequences of Measurable Line Fields
Mark Comerford
The no invariant line fields conjecture is one of the main outstanding problems in traditional complex dynamics. In this paper we consider non-autonomous iteration where one works…
Short Separating Geodesics for Multiply Connected Domains
Mark Comerford
We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, wh…
The Caratheodory Topology for Multiply Connected Domains II
Mark Comerford
We continue our exposition concerning the Caratheodory topology for multiply connected domains by introducing the notion of boundedness for a family of pointed domains of the same…