Let K be a closed subset of a smooth manifold M, and let f : K ! K be a continuous self-map of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism of the ambient space M. We give a necessary condition for the smoothability of the faithfully innnitely interval-renormalizable homeomorphisms of Cantor sets in the unit interval. This class contain...

The notation and terminology used in this paper are introduced in the following articles: [20], [21], [1], [3], [22], [4], [5], [19], [10], [18], [7], [17], [11], [2], [8], [9], [16], [13], [14], [15], [6], [23], and [12]. In this paper p1, p2 are points of E 2 T, C is a simple closed curve, and P is a subset of E T. Let n be a natural number, let A be a subset of En T, and let a, b be points o...