Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi - Pasta - Ulam lattices by the generalized alignment index method

C. Skokos, T. Bountis, C. Antonopoulos

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)

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 GALIk 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 GALIk 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.

Original languageEnglish
Pages (from-to)5-14
Number of pages10
JournalEuropean Physical Journal: Special Topics
Volume165
Issue number1
DOIs
Publication statusPublished - 2008

ASJC Scopus subject areas

  • Materials Science(all)
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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