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

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

2000-10-20

arxiv.org/abs/math/0010197v1

Mathematics

Dynamical Systems

9 pages. to appear in . Phys. A: Math. Gen. 33, 2000

Scientific paper

10.1088/0305-4470/34/11/311

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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