Cubic post-critically finite polynomials defined over $\mathbb{Q}$

17 Jun 2020  ·  Anderson Jacqueline, Manes Michelle, Tobin Bella ·

We describe and implement an algorithm to find all post-critically finite (PCF) cubic polynomials defined over $\mathbb{Q}$, up to conjugacy over $\text{PGL}_2(\bar{\mathbb{Q}})$. We describe normal forms that classify equivalence classes of cubic polynomials while respecting the field of definition... Applying known bounds on the coefficients of post-critically bounded polynomials to these normal forms simultaneously at all places of $\mathbb{Q}$, we create a finite search space of cubic polynomials over $\mathbb{Q}$ that may be PCF. Using a computer search of these possibly PCF cubic polynomials, we find fifteen which are in fact PCF. read more

PDF Abstract
No code implementations yet. Submit your code now


Number Theory Dynamical Systems