Linked orbits of homeomorphisms of the plane and Gambaudo–Kolev Theorem

Abstract Let h: R² R² be an orientation preserving homeomorphism of the plane. For any bounded orbit O (x) =\hⁿ (x): n\ there exists a fixed point p² of h linked to O (x) in the sense of Gambaudo: one cannot find a Jordan curve C² around O (x), separating it from p, that is isotopic to h (C) in R² (O (x) \p\).