Аннотация:We propose the hypothesis that the local integrability in sense (1) in all stationary points of autonomous planar systems of ordinary differential equations with polynomial right-hand sides and resolved with respect to derivatives leads to the existence of the global integral. If this system depends on parameters then it has a global integral in the case, when local integrability takes place for some set of parameters in all stationary points simultaneously.
If the system has invariant curves or separatrices the such integral can exist in the part of its phase space where the system is locally integrable at the neighborhoods of all stationary points.