Necessary Condition for the Existence of Algebraic First Integrals - Part One - Kowalevski's Exponents

Details Necessary Condition for the Existence of Algebraic First Integrals - Part One - Kowalevski's Exponents Necessary Condition for the Existence of Algebraic First Integrals - Part One - Kowalevski's Exponents

Dec 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..363y&link_type=abstract

Celestial Mechanics, Volume 31, Issue 4, pp.363-379

Mathematics

Dynamical Systems

109

Scientific paper

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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