Abstract
Existence of algebraic first integrals for a class of dynamical systems is discussed in connection with the nature of the singularities of solutions. It is shown that under some conditions, the existence of algebraic first integrals controls a quantity characterising a singularity (Kowalevski's exponent) which can be calculated in a finite procedure. Two simple examples are given, which illustrate how main theorems work.
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Yoshida, H. Necessary condition for the existence of algebraic first integrals. Celestial Mechanics 31, 363–379 (1983). https://doi.org/10.1007/BF01230292
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DOI: https://doi.org/10.1007/BF01230292