Finite-time rotation number: a fast indicator for chaotic dynamical structures

TL;DR

This paper introduces finite-time rotation numbers as a rapid alternative to finite-time Lyapunov exponents for detecting Lagrangian coherent structures in dynamical systems, applicable to both continuous and discrete cases.

Contribution

The paper demonstrates that finite-time rotation numbers can efficiently identify coherent structures, offering a faster method than traditional Lyapunov exponent calculations.

Findings

Finite-time rotation numbers effectively detect coherent structures.

The method applies to both continuous and discrete dynamical systems.

Finite-time rotation numbers are computationally faster than Lyapunov exponents.

Abstract

Lagrangian coherent structures are effective barriers, sticky regions, that separate phase space regions of different dynamical behavior. The usual way to detect such structures is via finite-time Lyapunov exponents. We show that similar results can be obtained for single-frequency systems from finite-time rotation numbers, which are much faster to compute. We illustrate our claim by considering examples of continuous and discrete-time dynamical systems of physical interest.