6 citations · 7 across the 6 of their papers we have counts for
7 papers
On the deck groups of iterates of bicritical rational maps
Sarah Koch, Kathryn Lindsey, Thomas Sharland
Given a rational map on the Riemann sphere, we define to be the group of Möbius transformations satisfying $f \…
Bicritical rational maps with a common iterate
Sarah Koch, Kathryn Lindsey, Thomas Sharland
Let be a degree bicritical rational map with critical point set and critical value set . Using the group of deck transfo…
Relations between Escape Regions in the Parameter Space of Cubic Polynomials
Araceli Bonifant, Chad Estabrooks, Thomas Sharland
We describe a topological relationship between slices of the parameter space of cubic maps. In the paper \cite{CP1}, Milnor defined the curves as the set of all cub…
Matings of cubic polynomials with a fixed critical point. Part II: -symmetry of limbs
Thomas Sharland
In this article we provide a combinatorial sufficient (and conjecturally, necessary) condition (called -symmetry) for the mating of two postcritically finite polynomials in $\ma…
Matings of Cubic polynomials with a fixed critical point, Part I: Thurston Obstructions
Thomas Sharland
We prove that if is a degree Thurston map with two fixed critical points, then any irreducible obstruction for contains a Levy cycle. As a corollary, it will be shown t…
Constructing rational maps with cluster points using the mating operation
Thomas Sharland
In this article, we show that all admissible rational maps with fixed or period two cluster cycles can be constructed by the mating of polynomials. We also investigate the polynomi…
Thurston equivalence for rational maps with clusters
Thomas Sharland
We investigate rational maps with period one and two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is and the cluster is fixed,…