TY - JOUR
T1 - HAUSDORFF DIMENSION of UNIVOQUE SETS of SELF-SIMILAR SETS with COMPLETE OVERLAPS
AU - Gareeb, Mohammad
AU - Li, Wenxia
N1 - Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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 .
AB - 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 .
KW - Configuration of Finite Pattern
KW - Graph-Directed Self-Similar Set
KW - Hausdorff Dimension
KW - Iterated Function System (IFS)
KW - Univoque Set
UR - https://www.scopus.com/pages/publications/85085090591
U2 - 10.1142/S0218348X20500516
DO - 10.1142/S0218348X20500516
M3 - 文章
AN - SCOPUS:85085090591
SN - 0218-348X
VL - 28
JO - Fractals
JF - Fractals
IS - 3
M1 - 2050051
ER -