We show that a planar unshielded compact set X is finitely Susli-nian if and only if there exists a closed set F ⊂ double-struck S sign1 and a lamination ̃ of F such that F/̃ is homeomorphic to X. If X is a continuum, the analogous statement follows from Carathéodory theory and is widely used in polynomial dynamics. © 2007 American Mathematical Society.
