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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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…

math.DS2017

Dynamical modular curves for quadratic polynomial maps

John R. Doyle

Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain cla…

math.DS2017★ 5 cited

Reduction of dynatomic curves

John R. Doyle, Holly Krieger, Andrew Obus +3

The dynatomic modular curves parametrize polynomial maps together with a point of period $n$ . It is known that the dynatomic curves $Y_{1} (n)$ are smooth and irreducible in character…

math.DS2016

Preperiodic portraits for unicritical polynomials over a rational function field

John R. Doyle

Let $K$ be an algebraically closed field of characteristic zero, and let $K := K (t)$ be the rational function field over $K$ . For each $d \geq 2$ , we consider the unicriti…

math.DS2015

Preperiodic portraits for unicritical polynomials

John R. Doyle

Let $K$ be an algebraically closed field of characteristic zero, and for $c \in K$ and an integer $d \geq 2$ , define $f_{d, c} (z) := z^{d} + c \in K [z]$ . We consider the following ques…