Lyapunov exponent for Lipschitz maps

TL;DR

This paper introduces a new way to define Lyapunov exponents using Lipschitz maps, extending dynamical systems analysis to non-differentiable functions and broadening its applicability.

Contribution

It proposes an alternative Lyapunov exponent definition based on Lipschitz maps, applicable to non-differentiable systems, and demonstrates that existing results remain valid.

Findings

Lyapunov exponents can be defined via Lipschitz maps.

Results from standard dynamical systems are applicable in this new context.

The approach broadens the scope of dynamical systems analysis.

Abstract

It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show that the results which are valid to standard discrete dynamical systems are also valid in this new context. Therefore, this novel approach expands the range of applications of the dynamical systems theory.