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Necessary conditions for the existence of particular algebraic first integrals

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Abstract

Existence of algebraic particular 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 particular first integrals controls a quantity characterising a singularity (Kowaleveski's exponent) which can be calculated in a finite procedure. Four examples are given which illustrate how main theorems work.

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  1. Mechanical Engineering Research Institute of Russian Academy of Sciences, Griboedova Str 4, 101830, Moscow, Russia

    V. V. Lunev

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  1. V. V. Lunev
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Lunev, V.V. Necessary conditions for the existence of particular algebraic first integrals. Celestial Mech Dyn Astr 61, 51–69 (1995). https://doi.org/10.1007/BF00051688

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  • DOI: https://doi.org/10.1007/BF00051688

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