Celestial Mechanics and Dynamical Astronomy

, Volume 73, Issue 1–4, pp 211–220 | Cite as

Detection of Ordered and Chaotic Motion Using the Dynamical Spectra

  • N. Voglis
  • G. Contopoulos
  • C. Efthymiopoulos

Abstract

Two simple and efficient numerical methods to explore the phase space structure are presented, based on the properties of the "dynamical spectra". 1) We calculate a "spectral distance" D of the dynamical spectra for two different initial deviation vectors. D → 0 in the case of chaotic orbits, while D → const ≠ 0 in the case of ordered orbits. This method is by orders of magnitude faster than the method of the Lyapunov Characteristic Number (LCN). 2) We define a sensitive indicator called ROTOR (ROtational TOri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational torus, while it tends to infinity at a rate ∝ N = number of iterations, in any case other than a rotational torus. We use this method to locate the last KAM torus of an island of stability, as well as the most important cantori causing stickiness near it.

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • N. Voglis
    • 1
  • G. Contopoulos
    • 1
    • 2
  • C. Efthymiopoulos
    • 1
    • 2
  1. 1.Department of AstronomyUniversity of AthensGreece
  2. 2.Department of AstronomyUniversity of AthensGreece

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