Abstract:

The authors considered the nonexistence of polynomial first integrals for quadratic planar vector fields, which can be treated as negative semihomogeneous systems. Using the Kowalevskaya exponents, we gave some simple criteria for the nonexistence of nontrivial polynomial first integrals for planar vector fields.

Key words:  planar vector field, semihomogeneous systems, first integral, Kowalevskaya exponent