Divergence of nearby trajectories for the gravitational N-body problem

Details Divergence of nearby trajectories for the gravitational N-body problem Divergence of nearby trajectories for the gravitational N-body problem

Dec 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990apj...364..420k&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 364, Dec. 1, 1990, p. 420-425.

Mathematics

24

Galactic Clusters, Gravitation Theory, Many Body Problem, Hamiltonian Functions, Jacobi Integral, Manifolds (Mathematics)

Scientific paper

This paper considers the Hamiltonian flow of a collection of N self-gravitating Newtonian point masses, viewed as a geodesic flow on an appropriate curved but conformally flat 3N-dimensional manifold. It is proved that, with respect to the natural Euclidean measure, the probability that a random perturbation of a random geodesic with comparable kinetic and potential energies will feel a positive curvature decreases exponentially to zero as N approaches infinity. This suggests that at least for short times, large self-gravitating systems should exhibit a 'mixing-type' or 'chaotic' behavior.

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