Cyclic coverings of the 3-sphere branched over wild knots of dynamically defined type

Let K be a tame knot and consider an n beaded necklace T. which is the union of n consecutive disjoint closed round balls (pearls) Bj, j = 1,..., n. An n pearl chain necklace T is the union of T. and K. We will construct, via the action of a Kleinian group, a sequence of nested pearl chain necklaces Tk whose inverse limit is a wild knot of dynamically defined type.(K, T0). In this paper, we will prove some topological properties of this kind of wild knots; in particular, we generalize the construction of cyclic branched coverings for this case, and we show that there exists a wild knot of dynamically defined type such that S3 is an n-fold cyclic branched covering of S3 along it, for n = 2.