Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2008-02-12
Nonlinear Sciences
Chaotic Dynamics
10 pages, 5 figures, submitted for publication in European Physical Journal - Special Topics. Revised version: Small explanato
Scientific paper
10.1140/epjst/e2008-00844-2
The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi--dimensional Hamiltonian systems. We propose an efficient computation of the GALI$_k$ indices, which represent volume elements of $k$ randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algorithm. We obtain theoretically and verify numerically asymptotic estimates of GALIs long--time behavior in the case of regular orbits lying on low--dimensional tori. The GALI$_k$ indices are applied to rapidly detect chaotic oscillations, identify low--dimensional tori of Fermi--Pasta--Ulam (FPU) lattices at low energies and predict weak diffusion away from quasiperiodic motion, long before it is actually observed in the oscillations.
Antonopoulos Chris
Bountis Tassos
Skokos Charalampos
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