Global dynamics of coupled standard maps
Abstract
Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-linear science. The Generalized ALignment Index (GALI), which was recently introduced and applied successfully for the distinction between regular and chaotic motion in Hamiltonian systems sk:6, is an ideal tool for this purpose. In the present paper we make a first step towards the dynamical study of multi--dimensional maps, by obtaining some interesting results for a 4--dimensional (4D) symplectic map consisting of N=2 coupled standard maps Kan:1. In particular, using the new GALI3 and GALI4 indices, we compute the percentages of regular and chaotic motion of the map equally reliably but much faster than previously used indices, like GALI2 (known in the literature as SALI).