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

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Published in Journal of Physics. A, Mathematical and General. 2001, vol. 34, no. 11, p. 2185-2193
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.
Stable URL http://archive-ouverte.unige.ch/unige:12387
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Deposited on : 2010-11-09

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