Global dynamics of coupled standard maps

Details Global dynamics of coupled standard maps Global dynamics of coupled standard maps

2008-01-25

arxiv.org/abs/0801.3923v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, to appear in the proceedings of the international conference "Chaos in Astronomy", Athens, Greece (poster

Scientific paper

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$_3$ and GALI$_4$ indices, we compute the percentages of regular and chaotic motion of the map equally reliably but much faster than previously used indices, like GALI$_2$ (known in the literature as SALI).

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