Vefa Goksel

activity

20132025

collaborators

12 papers

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.NT2023

A local-global conjugacy question arising from arithmetic dynamics

Vefa Goksel

In his earlier work, the author introduced a group theory question that arises in the study of iterated Galois groups of post-critically finite quadratic polynomials. In this paper…

math.NT2022

A note on the factorization of iterated quadratics over finite fields

Vefa Goksel

Let $f$ be a monic quadratic polynomial over a finite field of odd characteristic. In 2012, Boston and Jones constructed a Markov process based on the post-critical orbit of $f$ , a…

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.NT2022

Misiurewicz polynomials and dynamical units, Part I

Robert L. Benedetto, Vefa Goksel

We study the dynamics of the unicritical polynomial family $f_{d, c} (z) = z^{d} + c \in C [z]$ . The $c$ -values for which $f_{d, c}$ has a strictly preperiodic postcritical orbit are…

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…

math.NT2018

On the orbit of a post-critically finite polynomial of the form $x^{d} + c$

Vefa Goksel

In this paper, we study the critical orbit of a post-critically finite polynomial of the form $f_{c, d} (x) = x^{d} + c \in C [x]$ . We discover that in many cases the orbit eleme…

math.NT2017

Irreducibility of iterates of post-critically finite quadratic polynomials over $Q$

Vefa Goksel

In this paper, we classify, up to three possible exceptions, all monic, post-critically finite quadratic polynomials $f (x) \in Z [x]$ with an iterate reducible module every…

math.NT2013

A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields

Vefa Goksel, Shixiang Xia, Nigel Boston

Jones and Boston conjectured that the factorization process for iterates of irreducible quadratic polynomials over finite fields is approximated by a Markov model. In this paper, w…

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

The non-unit conjecture for Misiurewicz parameters

Square patterns in dynamical orbits

A local-global conjugacy question arising from arithmetic dynamics

A note on the factorization of iterated quadratics over finite fields

Misiurewicz polynomials and dynamical units, Part II

Misiurewicz polynomials and dynamical units, Part I

A note on Misiurewicz polynomials

Markov Processes and Some PCF Quadratic Polynomials

On the orbit of a post-critically finite polynomial of the form xd+c

Irreducibility of iterates of post-critically finite quadratic polynomials over Q

A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields

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

On the orbit of a post-critically finite polynomial of the form $x^{d} + c$

Irreducibility of iterates of post-critically finite quadratic polynomials over $Q$