Topological classification of limit periodic sets of polynomial planar vector fields

Abstract

We characterize the limit periodic sets of families of polynomial planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere with empty interior. Conversely, we show that any compact and connected semialgebraic set of the sphere with empty interior can be realized as a limit periodic set.