Reflections on the 'Saari Conjecture' and several new ones

Donald G. Saari

doi:10.3934/dcdss.2008.1.653

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2008, Volume 1, Issue 4: 653-665. Doi: 10.3934/dcdss.2008.1.653

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Reflections on the "Saari Conjecture" and several new ones

Donald G. Saari^1,

1.
Institute for Mathematical Behavioral Sciences, SSPA 2119, University of California, Irvine, CA 92697-5100

Received: December 31, 2005

Revised: June 30, 2008

Published: November 2008

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Abstract

After explaining what motivated an earlier, yet unanswered conjecture whether a constant moment of inertia requires a relative equilibrium motion, several related conjectures follow and are described. One of them would generalize the $N$-body Virial Theorem. The mathematical obstacle hindering solution of all of these issues is identified and discussed.

Keywords:

N-body problem.

Mathematics Subject Classification: Primary: 70F10, 70F15; Secondary: 85A05.

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