J. Doyle

activity

20112021

most citedPreperiodic points for quadratic polynomials over quadratic fields

12 citations · 38 across the 14 of their papers we have counts for

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Showing 2018Show all

4 papers · 1 filter

math.NT2018★ 4 cited

Moduli Spaces for Dynamical Systems with Portraits

John R. Doyle, Joseph H. Silverman

A $portrait$ $P$ on $P^{N}$ is a pair of finite point sets $Y \subseteq X \subset P^{N}$ , a map $Y \to X$ , and an assignment of weights to the points…

math.NT2018

Finite index theorems for iterated Galois groups of unicritical polynomials

Andrew Bridy, John R. Doyle, Dragos Ghioca +2

Let $K$ be the function field of a smooth, irreducible curve defined over $Q$ . Let $f \in K [x]$ be of the form $f (x) = x^{q} + c$ where $q = p^{r}, r \geq 1,$ is a powe…

math.NT2018★ 1 cited

A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on $P^{N}$

John R. Doyle, Joseph H. Silverman

Let $f : P^{N} \to P^{N}$ be an endomorphism of degree $d \geq 2$ defined over $Q$ or $Q_{p}$ , and let $K$ be the field of moduli of $f…

math.DS2018

Preperiodic points for quadratic polynomials over cyclotomic quadratic fields

John R. Doyle

Given a number field $K$ and a polynomial $f (z) \in K [z]$ of degree at least 2, one can construct a finite directed graph $G (f, K)$ whose vertices are the $K$ -rational preperiodic p…

Moduli Spaces for Dynamical Systems with Portraits

Finite index theorems for iterated Galois groups of unicritical polynomials

A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on PN

Preperiodic points for quadratic polynomials over cyclotomic quadratic fields

A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on $P^{N}$