Geodesic
On a Result of Bruns
Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 175-180

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Bruns' Theorem states that the classical integrals of the gravitational three-body problem generate all algebraic integrals. We show that the first step in his proof, together with Ziglin's non-integrability criterion for complex systems, can be used to prove the non-existence of energy independent algebraic integrals in certain real analytic systems. We also show that this aspect of Bruns' argument is purely algebraic: We offer a proof based on elementary differential algebraic methods.
DOI : 10.4153/CMB-1990-029-9
Mots-clés : S805, 70F07. 
Kummer, Martin; Churchill, Richard C.; Rod, David L. On a Result of Bruns. Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 175-180. doi: 10.4153/CMB-1990-029-9
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