Necessary Condition for the Existence of Algebraic First Integrals - Part Two - Condition for Algebraic Integrability

Details Necessary Condition for the Existence of Algebraic First Integrals - Part Two - Condition for Algebraic Integrability Necessary Condition for the Existence of Algebraic First Integrals - Part Two - Condition for Algebraic Integrability

Dec 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..381y&link_type=abstract

Celestial Mechanics, Volume 31, Issue 4, pp.381-399

Mathematics

Dynamical Systems

73

Scientific paper

Necessary condition for the existence of a sufficient number of algebraic first integrals is given for a class of dynamical systems. It is proved that in order that a given system is algebraically integrable, all possible Kowalevski's exponents, which characterize a singularity of the solution, must be rational number. For example, the classical 3-body problem and the Hénon-Heiles system are shown to be not algebraically integrable.

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