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arXiv · 0802.1646

Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method

Charalampos Skokos·Tassos Bountis·Chris Antonopoulos
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Abstract

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.

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Charalampos Skokos, Tassos Bountis, Chris Antonopoulos. 2008-03-10. Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method. https://doi.org/10.1140/epjst%2Fe2008-00844-2

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