Planar Analytic Nilpotent Germs Via Analytic First Integrals
MetadataShow full item record
We generalize the results of  by giving necessary and sufficient conditions for the planar analytic nilpotent germs to have an analytic first integral in (R, 0). The proof of our main result is based on a new method to compute the analytic first integrals of the nilpotent germs, the use of the weight homogeneous polynomials, and the method of characteristic curve for solving linear partial differential equations. Applications of our results to the Kukles-like cubic system are considered.