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On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations

Alexei Tsygvintsev
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Abstract

We consider systems of ordinary differential equations with quadratic homogeneous right hand side. We give a new simple proof of a result already obtained in [8,10] which gives the necessary conditions for the existence of polynomial first integrals. The necessary conditions for the existence of a polynomial symmetry field are given. It is proved that an arbitrary homogeneous first integral of a given degree is a linear combination of a fixed set of polynomials.

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Alexei Tsygvintsev. 2000-10-20. On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations. https://doi.org/10.1088/0305-4470%2F34%2F11%2F311

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