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We characterize the limit periodic sets of families of polynomial planarvector fields up to homeomorphisms. We show that any limit periodic set istopologically equivalent to a compact and connected semialgebraic set of thesphere with empty interior. Conversely, we show that any compact and connectedsemialgebraic set of the sphere with empty interior can be realized as a limitperiodic set.

Topological classification of limit periodic sets of polynomial planar vector fields