A survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane is presented. The theory is then extended to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus. The notion of a polynomial vector field on a regular surface and the notion of a first integral for such vector fields are defined.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|Publication status||Published - 1 Jan 2002|
- Polynomial vector fields