J. Doyle

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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 2015Show all

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math.NT2015

Preperiodic points for quadratic polynomials with small cycles over quadratic fields

John R. Doyle

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

math.NT2015

Configuration of the Crucial Set for a Quadratic Rational Map

John R. Doyle, Kenneth Jacobs, Robert Rumely

Let $K$ be a complete, algebraically closed non-archimedean valued field, and let $φ (z) \in K (z)$ have degree two. We describe the crucial set of $φ$ in terms of the multipliers of…

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…