Application of the Generalized Alignment Index (GALI) method to the dynamics of multi--dimensional symplectic maps

TL;DR

This paper demonstrates that the GALI method effectively differentiates between regular and chaotic dynamics in multi-dimensional symplectic maps, specifically applied to a system of three coupled standard maps.

Contribution

It introduces the application of the GALI method to multi-dimensional symplectic maps and shows its efficiency in identifying chaotic versus regular motion.

Findings

GALI rapidly distinguishes between regular and chaotic trajectories.

The method is effective for systems of N=3 coupled standard maps.

GALI provides a reliable criterion for phase space analysis.

Abstract

We study the phase space dynamics of multi--dimensional symplectic maps, using the method of the Generalized Alignment Index (GALI). In particular, we investigate the behavior of the GALI for a system of N=3 coupled standard maps and show that it provides an efficient criterion for rapidly distinguishing between regular and chaotic motion.