We characterize the limit periodic sets of families of algebraic 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 of dimension 0 or 1. Conversely, we show that any compact and connected semialgebraic set of the sphere of dimension 0 or 1 can be realized as a limit periodic set.
André Belotto da Silva. Jose Ginés Espín Buendía. "Topological classification of limit periodic sets of polynomial planar vector fields." Publ. Mat. 63 (1) 105 - 123, 2019. https://doi.org/10.5565/PUBLMAT6311903