Local behavior of planar analytic vector fields via integrability
A method to study the behaviour of trajectories near a singular point in planar analytic systems of the form \[ \dot{x}=P(x,y),\;\;\dot{y}=Q(x,y) \] is presented. It can be applied provided the system has a first integral which is a quotient of analytic functions. In particular, the method can be applied to vector fields with a rational first integral. Examples illustrate the method.
scientific article; zbMATH DE number 5962606