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


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.


Phase Space Sensitive Indicator Space Structure Chaotic Motion Dynamical Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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