5 citations · 7 across the 11 of their papers we have counts for
12 papers
Thick-Thin non-Autonomous Julia Sets
Mark Comerford, Hiroki Sumi
Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in \cite{SSS} who gave several examples of such sets based on Cantor set-like constru…
Mandelbrot sets for fixed template iterations
Mark Comerford, Anca Radulescu, Kieran Cavanagh
We study the dynamics of template iterations, consisting of arbitrary compositions of functions chosen from a finite set of polynomials. In particular, we focus on templates using…
Hereditarily non Uniformly Perfect non-Autonomous Julia Sets
Mark Comerford, Rich Stankewitz, Hiroki Sumi
Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in \cite{SSS} who gave several examples of such sets based on Cantor set-like constru…
On Possible Limit Functions on a Fatou Component in non-Autonomous Iteration
Mark Comerford, Christopher Staniszewski
The possibilities for limit functions on a Fatou component for the iteration of a single polynomial or rational function are well understood and quite restricted. In non-autonomous…
Orbit Portraits in non-Autonomous Iteration
Mark Comerford, Todd Woodard
We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic ver…
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…