December  2008, 1(4): 653-665. doi: 10.3934/dcdss.2008.1.653

Reflections on the "Saari Conjecture" and several new ones

1. 

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

Received  January 2006 Revised  July 2008 Published  September 2008

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.
Citation: Donald G. Saari. Reflections on the "Saari Conjecture" and several new ones. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 653-665. doi: 10.3934/dcdss.2008.1.653
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