HAUSDORFF DIMENSION OF UNIVOQUE SETS OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS

摘要

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