Dynamics of Chebyshev polynomials on $\mathbb{Z}_{2}$

TL;DR

This paper fully characterizes the dynamical behavior of Chebyshev polynomials over the 2-adic integers, identifying all minimal subsystems and their basins of attraction.

Contribution

It provides a complete description of the minimal components and attractors for Chebyshev polynomials on rac{rac{rac{}

Findings

All minimal subsystems identified.

Attracting basins characterized.

Dynamical structure fully described.

Abstract

The dynamical structure of Chebyshev polynomials on $\mathbb{Z}_2$, the ring of $2$-adic integers, is fully described by showing all its minimal subsystems and their attracting basins.