Planar analytic systems having locally analytic first integrals at an isolated singular point

摘要

The aim of this paper is to answer the open problem 3 posed by Chavarriga et al (1999 J. Diff. Eqns 157 163-82). The problem is to characterize analytic systems having an isolated singular point formed by hyperbolic sectors which are C-omega locally integrable at this singular point.