Abstract
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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Yoshida, H. Necessary condition for the existence of algebraic first integrals. Celestial Mechanics 31, 381–399 (1983). https://doi.org/10.1007/BF01230293
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DOI: https://doi.org/10.1007/BF01230293