Chaos, Regularity, and Noise in Self-Gravitating Systems

Details Chaos, Regularity, and Noise in Self-Gravitating Systems Chaos, Regularity, and Noise in Self-Gravitating Systems

1994-10-28

arxiv.org/abs/astro-ph/9410091v1

Astronomy and Astrophysics

Astrophysics

19 pages, LaTeX, Invited plenary talk at the Seventh Marcel Grossmann Meeting July 1994

Scientific paper

This paper summarises a number of new, potentially significant, results, obtained recently by the author and his collaborators, which impact on various issues related to the gravitational N-body problem, both Newtonianly and in the context of general relativity. Topics addressed include: (1) direct N-body simulations and their interpretation, with reference to the observed exponential instability towards small changes in initial conditions and the phenomenon of ``nonviolent relaxation;'' (2) the Hamiltonian structure of the collisionless Boltzmann equation of general relativity, i.e., the Vlasov-Einstein system; (3) ``transient ensemble dynamics,'' i.e.,,the short time statistical characterisation of collections of orbits in nonintegrable mean field potentials; and (4) the structural stability of the smooth potential approximation typically used in galactic dynamics.

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