Thomas Sharland

activity

20112022

most citedConstructing rational maps with cluster points using the mating operation

6 citations · 7 across the 6 of their papers we have counts for

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Showing 2022Show all

4 papers · 1 filter

math.DS2022

On the deck groups of iterates of bicritical rational maps

Sarah Koch, Kathryn Lindsey, Thomas Sharland

Given a rational map $f : C \to C$ on the Riemann sphere, we define $Deck (f)$ to be the group of Möbius transformations $μ$ satisfying $f \…

math.DS2022

Bicritical rational maps with a common iterate

Sarah Koch, Kathryn Lindsey, Thomas Sharland

Let $f$ be a degree $d$ bicritical rational map with critical point set $C_{f}$ and critical value set $V_{f}$ . Using the group $Deck (f^{k})$ of deck transfo…

math.DS2022

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 $S_{n}$ as the set of all cub…

math.DS2022★ 1 cited

Matings of cubic polynomials with a fixed critical point. Part II: $α$ -symmetry of limbs

Thomas Sharland

In this article we provide a combinatorial sufficient (and conjecturally, necessary) condition (called $α$ -symmetry) for the mating of two postcritically finite polynomials in $\ma…

On the deck groups of iterates of bicritical rational maps

Bicritical rational maps with a common iterate

Relations between Escape Regions in the Parameter Space of Cubic Polynomials

Matings of cubic polynomials with a fixed critical point. Part II: α-symmetry of limbs

Matings of cubic polynomials with a fixed critical point. Part II: $α$ -symmetry of limbs