5 citations · 7 across the 11 of their papers we have counts for
8 papers · 1 filter
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…
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…