HAUSDORFF DIMENSION of UNIVOQUE SETS of SELF-SIMILAR SETS with COMPLETE OVERLAPS

Let λ (0, 1) and m ≥ 3 an integer. We consider the collection of homogeneous self-similar sets on the line such that every two of copies fi(K),fj(K) of the self-similar set K are either separated or overlapped with rank k in {2,...,m}. For K generated by n similitudes, we denote by nj the number of overlaps with rank j {2,...,m}. The set of points in the self-similar set having a unique coding is called the univoque set and denoted by . In this paper, we investigate a uniform method to calculate the Hausdorff dimension of the set .