Heidi Benham
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View article: The Ginsburg--Sands theorem and computability theory
The Ginsburg--Sands theorem and computability theory Open
The Ginsburg--Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on $ω$: indiscrete, discrete, initial segment, final segment, and …
View article: Integrality and Thurston Rigidity for Bicritical PCF Polynomials
Integrality and Thurston Rigidity for Bicritical PCF Polynomials Open
We give an algebraic proof of an important consequence of Thurston rigidity for bicritical PCF polynomials with periodic critical points under certain mild assumptions. The key result is that when the family of bicritical polynomials is pa…
View article: Two New Normals Forms for Polynomial Endomorphisms of the Projective Line with Applications to Postcritically Finite Maps
Two New Normals Forms for Polynomial Endomorphisms of the Projective Line with Applications to Postcritically Finite Maps Open
We explore two normal forms for polynomial endomorphisms of the projective line. The first is a normal form for degree 3 polynomials in terms of the multipliers of the fixed points. This normal form allows for an enumeration of all $K$-rat…
View article: New Normal Forms For Degree Three Polynomials and Rational Functions
New Normal Forms For Degree Three Polynomials and Rational Functions Open
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared…