Vefa Goksel

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20182025

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math.NT2025

Iterates of post-critically finite polynomials of the form $x^{d} + c$

Vefa Goksel

Fix a prime number $d$ . The post-critically finite polynomials of the form $f_{d, c} = x^{d} + c \in C [x]$ play a fundamental role in polynomial dynamics. While many results are…

math.NT2025

The non-unit conjecture for Misiurewicz parameters

Robert L. Benedetto, Vefa Goksel

A Misiurewicz parameter is a complex number $c$ for which the orbit of the critical point $z = 0$ under $z^{2} + c$ is strictly preperiodic. Such parameters play the same role as special…

math.NT2024

Square patterns in dynamical orbits

Vefa Goksel, Giacomo Micheli

Let $q$ be an odd prime power. Let $f \in F_{q} [x]$ be a polynomial having degree at least $2$ , $a \in F_{q}$ , and denote by $f^{n}$ the $n$ -th iteration of $f$ . Let $χ$ …

math.NT2022

Misiurewicz polynomials and dynamical units, Part II

Robert L. Benedetto, Vefa Goksel

Fix an integer $d \geq 2$ . The parameters $c_{0} \in Q ˉ$ for which the unicritical polynomial $f_{d, c} (z) = z^{d} + c \in C [z]$ has finite postcritical orbit, also know…

math.NT2019

A note on Misiurewicz polynomials

Vefa Goksel

Let $f_{c, d} (x) = x^{d} + c \in C [x]$ . The $c_{0}$ values for which $f_{c_{0}, d}$ has a strictly pre-periodic finite critical orbit are called Misiurewicz points. Any Misiurewicz poi…

math.NT2018

Markov Processes and Some PCF Quadratic Polynomials

Vefa Goksel

For any $n \geq 1$ , let $T_{n}$ be the complete binary rooted tree of height $n$ , and $f (x) = (x + a)^{2} - a - 1$ such that $a \neq = \pm b^{2}$ for any $b \in Z$ . In \cite{Settled}, Jones…

Iterates of post-critically finite polynomials of the form xd+c

The non-unit conjecture for Misiurewicz parameters

Square patterns in dynamical orbits

Misiurewicz polynomials and dynamical units, Part II

A note on Misiurewicz polynomials

Markov Processes and Some PCF Quadratic Polynomials

Iterates of post-critically finite polynomials of the form $x^{d} + c$