TY - JOUR
T1 - Darboux integrability for the Rössler system
AU - Llibre, Jaume
AU - Zhang, Xiang
PY - 2002/1/1
Y1 - 2002/1/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/0036333815
U2 - 10.1142/S0218127402004474
DO - 10.1142/S0218127402004474
M3 - Article
SN - 0218-1274
VL - 12
SP - 421
EP - 428
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
ER -