The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy

TL;DR

The paper explores the Relative Lyapunov Indicator (RLI), demonstrating its effectiveness in identifying chaos and order in dynamical systems, with applications in dynamical astronomy and comparisons to other chaos detection methods.

Contribution

It provides a comprehensive analysis of the RLI's theoretical basis, compares it with other indicators, and showcases its practical applications in dynamical astronomy.

Findings

RLI efficiently distinguishes between ordered and chaotic orbits.

It outperforms some existing chaos indicators in certain scenarios.

The method is successfully applied to problems in dynamical astronomy.

Abstract

A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in determining the true nature of individual orbits, and in separating ordered and chaotic regions of the phase space of dynamical systems. A comparison between the RLI and some other variational indicators are presented, as well as the recent applications of the RLI to various problems of dynamical astronomy.