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Bruns’ theorem: The proof and some generalizations. (English) Zbl 0993.70012

The author considers Bruns’ theorem of 1887 concerning the integrals of motion for many-particle systems. Following work by Poincaré, the author points out that there are deficiencies and lack of rigour in many previous proofs of this theorem. The author generalizes the theorem to the case of \(n+1\) bodies in \(\mathbb{R}^\rho\), \(\rho\leq n+1\), and provides a rigorous proof of the theorem, paying particular attention to certain special cases. An extension of the theorem is made to include explicit time dependence, and a generalization of the theorem previously given with an erroneous proof by Painlevé, is stated but is not proved. The work arises from a doctoral thesis at Paris VII University.

MSC:

70F10 \(n\)-body problems
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