Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method
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 indices, which represent volume elements of 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 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.
Keywords
Cite
@article{arxiv.0802.1646,
title = {Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method},
author = {Charalampos Skokos and Tassos Bountis and Chris Antonopoulos},
journal= {arXiv preprint arXiv:0802.1646},
year = {2009}
}
Comments
10 pages, 5 figures, submitted for publication in European Physical Journal - Special Topics. Revised version: Small explanatory additions to the text and addition of some references. A small figure change