Complex statistics in Hamiltonian barred galaxy models

Tassos Bountis, Thanos Manos, Chris Antonopoulos

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We use probability density functions (pdfs) of sums of orbit coordinates, over time intervals of the order of one Hubble time, to distinguish weakly from strongly chaotic orbits in a barred galaxy model. We find that, in the weakly chaotic case, quasi-stationary states arise, whose pdfs are well approximated by q-Gaussian functions (with 1 < q < 3), while strong chaos is identified by pdfs which quickly tend to Gaussians (q = 1). Typical examples of weakly chaotic orbits are those that "stick" to islands of ordered motion. Their presence in rotating galaxy models has been investigated thoroughly in recent years due to their ability to support galaxy structures for relatively long time scales. In this paper, we demonstrate, on specific orbits of 2 and 3 degree of freedom barred galaxy models, that the proposed statistical approach can distinguish weakly from strongly chaotic motion accurately and efficiently, especially in cases where Lyapunov exponents and other local dynamic indicators appear to be inconclusive.

Original languageEnglish
Pages (from-to)63-80
Number of pages18
JournalCelestial Mechanics and Dynamical Astronomy
Issue number1
Publication statusPublished - May 2012


  • Chaotic motions
  • Hamiltonian systems
  • Numerical methods
  • Statistical methods
  • Stellar systems

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics

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