noninvertible maps of the plane. The invariant sets we consider are unstable manifolds of
saddle-type fixed and periodic points, as well as attracting invariant circles. Since for such
maps a point may have more than one first-rank preimages, the geometry, transitions, and
general properties of these sets are more complicated than the corresponding sets for
diffeomorphisms. The critical curve (s)(locus of points having at least two coincident …