5 papers
Indecomposable translates and degree- points
Alexander Galarraga
A curve over a number field has infinitely many degree- points if and only if there exists a degree- - or -parametrized point. We show that a …
Cubic points on dynamical modular curves
John R. Doyle, Alexander Galarraga
We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use t…
Superelliptic degree sets over Henselian fields
Alexander Galarraga, Alexander Wang
Let be a discretely valued Henselian field. Creutz and Viray show that the degree set of a curve over a -adic field can miss infinitely many multiples of the index of $C…
Integrality and Thurston Rigidity for Bicritical PCF Polynomials
Heidi Benham, Alexander Galarraga, Benjamin Hutz +3
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 res…
New Normal Forms For Degree Three Polynomials and Rational Functions
Heidi Benham, Alexander Galarraga, Benjamin Hutz +3
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 que…