Analytic nilpotent centers with analytic first integral
This paper considers an analytic system having an isolated nilpotent singularity at the origin: \[ \dot{x}=y+X_2(x,y), \dot{y}=Y_2(x,y). \] A necessary condition for local analytic integrability is given. The condition can be verified using the normal form theory.
scientific article; zbMATH DE number 5687535