Benedetto's trick and existence of rational preperiodic structures for quadratic polynomials

TL;DR

This paper refines Benedetto's p-adic analysis result to demonstrate infinitely many quadratic polynomials with rational coefficients that have a predetermined structure of rational preperiodic points.

Contribution

It introduces a refined method to construct quadratic polynomials with specific rational preperiodic structures, expanding understanding of rational preperiodic points.

Findings

Existence of infinitely many quadratic polynomials with given rational preperiodic graphs.

Refinement of Benedetto's p-adic analysis technique.

Explicit construction of polynomials with prescribed preperiodic structures.

Abstract

We refine a result of R. Benedetto in p-adic analysis in order to exhibit infinitely many quadratic polynomials with rational coefficients having a specified graph of rational preperiodic points.