A first approach to the Galois group of chaotic chains

TL;DR

This paper introduces a novel approach to defining and constructing the Galois group for chaotic chains, extending classical polynomial Galois theory to chaotic dynamical systems, with initial focus on degree 2 cases.

Contribution

It generalizes the concept of Galois groups from Chebyshev polynomials to chaotic chains, providing a foundational framework for future research.

Findings

Galois group construction for degree 2 chaotic chains

Detailed methodology for Chebyshev polynomial analysis

Initial insights into extending Galois theory to chaos

Abstract

We explain in detail the definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galois group of chaotic chains. The calculations in this paper are performed for Chebyshev polynomials and chaotic chains of degree $N=2$. Insides into possible further steps are given.