The stable subset of a univalent self-map

We give a complete description of the stable subset (the union of all backward orbit with bounded step) and of the pre-models of a univalent self-map f : X → X , where X is a Kobayashi hyperbolic cocompact complex manifold, such as the ball or the polydisc in C q . The result is obtained studying the complex structure of a decreasing intersection of complex manifolds, all biholomorphic to X .