Subexponential instability implies infinite invariant measure

TL;DR

This paper investigates the nature of weak chaos in dynamical systems, demonstrating that subexponential instability is linked to an infinite invariant measure and introducing a generalized Lyapunov exponent for characterization.

Contribution

It establishes a connection between subexponential instability and infinite invariant measures, and proposes a generalized Lyapunov exponent for analyzing such systems.

Findings

Subexponential instability implies an infinite invariant measure.

A generalized Lyapunov exponent effectively characterizes subexponential instability.

Weak chaos can be described by these new theoretical insights.

Abstract

We study subexponential instability to characterize a dynamical instability of weak chaos. We show that a dynamical system with subexponential instability has an infinite invariant measure, and then we present the generalized Lyapunov exponent to characterize subexponential instability.