Smaller alignment index (SALI): Determining the ordered or chaotic nature of orbits in conservative dynamical systems

Details Smaller alignment index (SALI): Determining the ordered or chaotic nature of orbits in conservative dynamical systems Smaller alignment index (SALI): Determining the ordered or chaotic nature of orbits in conservative dynamical systems

2002-10-23

arxiv.org/abs/nlin/0210053v1

Nonlinear Sciences

Chaotic Dynamics

9 pages, 5 figures, to appear in "Proceedings of International Conference on Libration Point Orbits and Applications" Aiguabla

Scientific paper

We apply the smaller alignment index (SALI) method for distinguishing between ordered and chaotic motion in some simple conservative dynamical systems. In particular we compute the SALI for ordered and chaotic orbits in a 2D and a 4D symplectic map, as well as a two--degree of freedom Hamiltonian system due to H\'{e}non & Heiles. In all cases, the SALI determines correctly the nature of the tested orbit, faster than the method of the computation of the maximal Lyapunov characteristic number. The computation of the SALI for a sample of initial conditions allows us to clearly distinguish between regions in phase space where ordered or chaotic motion occurs.

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