On the Lyapunov numbers

TL;DR

This paper introduces Lyapunov numbers as measures of sensitivity in dynamical systems and proves that in minimal weakly mixing systems, all Lyapunov numbers are equal.

Contribution

It defines Lyapunov numbers for dynamical systems and establishes a key property for minimal weakly mixing systems.

Findings

All Lyapunov numbers are equal in minimal weakly mixing systems

Lyapunov numbers quantify sensitivity in dynamical systems

Provides a new measure for analyzing system sensitivity

Abstract

We introduce and study the Lyapunov numbers -- quantitative measures of the sensitivity of a dynamical system $(X,f)$ given by a compact metric space $X$ and a continuous map $f:X \to X$. In particular, we prove that for a minimal topologically weakly mixing system all Lyapunov numbers are the same.