Application of the GALI method to localization dynamics in nonlinear systems

T. Bountis, T. Manos, H. Christodoulidi

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We investigate localization phenomena and stability properties of quasiperiodic oscillations in N degree of freedom Hamiltonian systems and N coupled symplectic maps. In particular, we study an example of a parametrically driven Hamiltonian lattice with only quartic coupling terms and a system of N 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.

Original languageEnglish
Pages (from-to)17-26
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume227
Issue number1
DOIs
Publication statusPublished - May 1 2009

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Keywords

  • Chaotic motion
  • Dimension of tori
  • Discrete breathers
  • GALI method
  • Hamiltonian systems
  • Quasiperiodic motion
  • Standard map
  • Symplectic maps

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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