Computation of Finite Time Lyapunov Exponents using the Perron-Frobenius operator

TL;DR

This paper introduces a method to compute finite time Lyapunov exponents using the Perron-Frobenius operator, aiming to unify two key tools for analyzing phase space transport.

Contribution

It presents a novel methodology to derive FTLE from the Perron-Frobenius operator, bridging a gap between geometric and probabilistic approaches.

Findings

Provides a new computational approach for FTLE using Perron-Frobenius operator

Facilitates integration of geometric and probabilistic methods in phase space analysis

Enhances understanding of phase space transport mechanisms

Abstract

The problem of phase space transport which is of interest both theoretically and from the point of view of applications has been investigated extensively using geometric and probabilistic methods. Two of the important tools for this that emerged in the last decade are the Finite time Lyapunov exponents (FTLE) and the Perron-Frobenius operator. The relationship between these approaches has not been clearly understood so far. In this paper a methodology is presented to compute the FTLE from the Perron-Frobenius operator, thus providing a step towards combining both the methods into a common framework.