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On a Result of Bruns

Published online by Cambridge University Press:  20 November 2018

Martin Kummer ,
Richard C. Churchill  and
David L. Rod
Martin Kummer
Affiliation:
Department of Mathematics, University of Toledo, Toledo, Ohio, 43606, U.S.A.
Richard C. Churchill
Affiliation:
Hunter College (CUNY), 695 Park Avenue, New York, NY., 10021, U.S.A.
David L. Rod
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
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Abstract

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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.

Keywords

S80570F07.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 175 - 180
Copyright
Copyright © Canadian Mathematical Society 1990

References

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