On the integrability of the N-body problem

Details On the integrability of the N-body problem On the integrability of the N-body problem

Aug 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986sval...12..235s&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 12, July 1986, p. 557-561) Soviet Astronomy Letters (ISSN 0360-0327), vol. 12, July-Aug

Astronomy and Astrophysics

Astronomy

Many Body Problem, Numerical Integration, Equations Of Motion, Kepler Laws, Solar Orbits

Scientific paper

Away from close approaches, and for large enough kinetic energies, circumstances exist such that the equations of motion of the N-body problem are exactly integrable. The existence of solutions covering an unbounded time interval is proved; the qualitative behavior of the flow in phase space is determined, and a sequence is constructed that converges locally uniformly to the solution in a domain comprising the complete time-axis multipled by an initial-value domain whose structure is fairly simple. Taken together, such domains will have an infinite volume.

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