Some families of polynomials satisfying uniform boundedness for rational preperiodic points

TL;DR

This paper constructs explicit families of polynomials over the rational numbers that demonstrate uniform boundedness in the number of rational preperiodic points, advancing understanding in arithmetic dynamics.

Contribution

It introduces new explicit non-isotrivial polynomial families over ield with proven uniform bounds on rational preperiodic points.

Findings

Explicit non-isotrivial polynomial families over ield

Proof of uniform boundedness for rational preperiodic points

Advancement in arithmetic dynamics theory

Abstract

We construct explicit non-isotrivial families of polynomials over $\mathbb{Q}$ satisfying uniform boundedness for their rational preperiodic points.