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
Externally publishedYes

Fingerprint

Hamiltonians
Nonlinear systems
Alignment
Nonlinear Systems
Standard Map
Coupled Maps
Quartic
Hamiltonian Systems
Dimensionality
Numerical methods
Torus
Orbits
Orbit
Degree of freedom
Numerical Methods
Oscillation
Term

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

Cite this

Application of the GALI method to localization dynamics in nonlinear systems. / Bountis, T.; Manos, T.; Christodoulidi, H.

In: Journal of Computational and Applied Mathematics, Vol. 227, No. 1, 01.05.2009, p. 17-26.

Research output: Contribution to journalArticle

Bountis, T. ; Manos, T. ; Christodoulidi, H. / Application of the GALI method to localization dynamics in nonlinear systems. In: Journal of Computational and Applied Mathematics. 2009 ; Vol. 227, No. 1. pp. 17-26.
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