Periodic points in towers of finite fields for polynomials associated to algebraic groups

TL;DR

This paper investigates the asymptotic behavior of periodic points in finite field towers for specific polynomial maps linked to algebraic groups, such as power maps and Chebyshev polynomials.

Contribution

It provides the limiting proportions of periodic points in these towers for the first time, focusing on algebraic group-related polynomial maps.

Findings

Limiting proportion of periodic points for z^d maps

Limiting proportion for Chebyshev polynomials

Results applicable to towers of finite fields

Abstract

We find the limiting proportion of periodic points in towers of finite fields for polynomial maps associated to algebraic groups, namely pure power maps z^d and Chebyshev polynomials.