Qualitative Theory of Planar Differential Systems

Our aim is to study ordinary differential equations or simply differential systems in two real variables x— = P(x,y), (0.1) y? = Q(x,y), r 2 where P and Q are C functions defined on an open subset U of R , with— r=1,2,...,?,?.AsusualC standsforanalyticity.Weputspecialemphasis onto polynomial differential systems, i.e., on systems (0.1) where P and Q are polynomials. Instead of talking about the differential system (0.1), we frequently talk about its associated vector field—— X = P(x,y) +Q(x...