A differential algorithm for the Lyapunov spectrum

TL;DR

This paper introduces a novel continuous differential algorithm for computing the Lyapunov spectrum that avoids rescaling issues, demonstrated through a particle dynamics example.

Contribution

A new matrix differential equation-based method for Lyapunov spectrum calculation that eliminates the need for rescaling or realignment.

Findings

The algorithm computes Lyapunov exponents without divergence issues.

Advantages include continuous rate of expansion calculation.

Drawbacks are discussed with a particle between contracting walls example.

Abstract

We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so called continuous type, where the rate of expansion of perturbations is obtained for all times, and the exponents are reached as the limit at infinity. It does not involve exponentially divergent quantities so there is no need of rescaling or realigning of the solution. We show the algorithm's advantages and drawbacks using mainly the example of a particle moving between two contracting walls.