Invariant curves and analytic integrability of a planar vector field (Q1627706)

The paper contains an excessive number of results, stated in 21 theorems, 5 propositions, 2 lemmas and 4 examples. The authors deal with planar vector fields \(\mathbf{F}=(P,Q)^\top\) which are analytic near the isolated singularity at the origin. The results in the paper concern such things as the existence of irreducible invariant curves, the analytic integrability (or non-integrability), the existence of algebraic inverse integrating factors, etc. Most of the results are related to the quasi-homogeneous case. The introductory part has very useful review of previous results on the topic.