Application of the GALI Method to Localization Dynamics in Nonlinear Systems
arXiv:0806.3563 · doi:10.1016/j.cam.2008.07.034
Abstract
We investigate localization phenomena and stability properties of quasiperiodic oscillations in degree of freedom Hamiltonian systems and coupled symplectic maps. In particular, we study an example of a parametrically driven Hamiltonian lattice with only quartic coupling terms and a system of coupled standard maps. We explore their dynamics using the Generalized Alignment Index (GALI), which constitutes a recently developed numerical method for detecting chaotic orbits in many dimensions, estimating the dimensionality of quasiperiodic tori and predicting slow diffusion in a way that is faster and more reliable than many other approaches known to date.
16 pages, 8 figures, submitted for publication in Journal of Computational and Applied Mathematics (Elsevier)
References in corpus (4)
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