Ergodic methods in stellar dynamics View Full Text


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Chapter Info

DATE

1994

AUTHORS

V. G. Gurzadyan

ABSTRACT

What are the main advantages of the present treatment of stellar dynamics from the point of view of theory of dynamcal systems? Another example is the term chaos: only systems possessing at least the property of mixing, and not purely ergodic ones, can be called chaotic, e.g., such terms as ergodic chaos should be considered as having no meaning. Spherical stellar systems can thus be designated as chaotic systems. The second advantage is the possibility of obtaining deeper insight into the fundamental properties of N-body systems and the discovery of underlying relationships between them. The relations between the negativity of the two-dimensional curvature determined by the Newtonian interaction potential, the exponential instability of phase trajectories and relaxation driving effects for spherical stellar systems, the properties of Lie groups, and the conclusion regarding the exponential instability of flow (but not relaxation) in the consideration of disk systems, are examples of this fact. The absence of a universal relaxation time scale indicates that the attempts to estimate relaxation time scales which describe the observed states of galaxies and star clusters by using numerical simulations of 100 or 1000 or even more particle models of N-body systems with a somehow softened potential cannot make much sense. In particular, the exponential growth of errors in gravitating N-body systems as first found by Miller [20]|cannot be directly related to relaxation time scales since the same effect can be seen, for example, in the integrable 2-body Kepler problem (for the discussion of N-body numerical simulations see [21,22]). Studies already completed indicate that the Ricci curvature method can be a useful tool for numerically investigating the local (in time) instability properties not only of stellar configurations, but also of plasma and other many-dimensional systems. Finally, this approach offers more unsolved problems, some of which are listed in [3], than those which are presently solvable. I think this can be considered as another advantage rather than as a weak point of this technique. More... »

PAGES

41-55

References to SciGraph publications

  • 1987-05. Disk galaxies and dynamical systems with non-negative curvature in ASTROPHYSICS AND SPACE SCIENCE
  • 1987-07. Relative chaos in stellar systems in ASTROPHYSICS AND SPACE SCIENCE
  • Book

    TITLE

    Ergodic Concepts in Stellar Dynamics

    ISBN

    3-540-57929-X

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bfb0058089

    DOI

    http://dx.doi.org/10.1007/bfb0058089

    DIMENSIONS

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