Global dynamics of coupled standard maps
arXiv:0801.3923 · doi:10.1007/978-3-540-75826-6_38
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 \cite{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 \cite{Kan:1}. In particular, using the new GALI and GALI indices, we compute the percentages of regular and chaotic motion of the map equally reliably but much faster than previously used indices, like GALI (known in the literature as SALI).
arXiv comment4 pages, 3 figures, to appear in the proceedings of the international conference "Chaos in Astronomy", Athens, Greece (poster contribution)