Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.2, pp.171-176

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.2, pp.171-176

Studying the Global Dynamics of Conservative Dynamical Systems Using the SALI Chaos Detection Method.
T. Manos, Ch. Skokos, E. Athanassoula, and T. Bountis

We use the Smaller ALignment Index (SALI) method of chaos detection, to study the global dynamics of conservative dynamical systems described by differential or difference equations. In particular, we consider the well-known 2-dimensional standard map and autonomous Hamiltonian systems of 2 and 3 degrees of freedom describing the motion of a star in models of barred galaxies. The application of SALI helped us to compute rapidly and accurately the percentage of regular and chaotic motion for particular values of the parameters of these systems. We were also able to perform a computationally efficient determination of the dependence of these percentages on the variation of various parameters of the studied models.
Key words: symplectic maps, hamiltonian systems, standard map, barred galactic potentials, chaotic motion, regular motion, SALI method

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