In this note we characterize all generators of Darboux polynomials of the Rössler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. As a corollary we prove that the Rössler system is not algebraically integrable, and that every rational first integral is a rational function in the variable x2+y2+2z. Moreover, we characterize the topological phase portrait of the Darboux integrable Rössler system.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|Publication status||Published - 1 Jan 2002|