MSc.Thesis Defense:Kader Bulut

POLYNOMIALS WITH RATIONAL PREPERIODIC POINTS

Kader Bulut
Mathematics, MSc. Thesis Dissertation, 2024

Thesis Jury

Assoc. Prof Mohammad Sadek (Thesis Advisor),

Asst. Prof. Nurdagül Anbar Meidl

Asst. Prof. Nermine Ahmed El Sissi

Date & Time: 19th, 2014 –  11:00 AM

Place: FASS 1096

Keywords : Arithmetic dynamics, elliptic curves, hyperelliptic curves, abelian

varieties, preperiodic points, periodic points

Abstract

In this thesis we focus on the preperiodic and periodic points of the dynamical systems associated to rational maps of degree 2. We discuss the state of the art regarding rational preperiodic points of polynomials of degree 2 defined over the rational field with an emphasis on the Uniform Boundedness Conjecture on the number of such points. We then study the known classification results of rational

preperiodic points of rational maps of degree 2, these maps include rational maps of degree 2 with abelian automorphism groups and rational maps of degree 2 with a rational periodic critical point of period 2.