A Generalized Finite Type Condition for Iterated Function Systems
Document Type
Article
Publication Date
1-30-2007
Publication Title
Advances in Mathematics
DOI
10.1016/j.aim.2006.03.007
ISSN
0001-8708
Abstract
We study iterated function systems (IFSs) of contractive similitudes on Rd with overlaps. We introduce a generalized finite type condition which extends a more restrictive condition in [S.-M. Ngai, Y. Wang, Hausdorff dimension of self-similar sets with overlaps, J. London Math. Soc. (2) 63 (3) (2001) 655–672] and allows us to include some IFSs of contractive similitudes whose contraction ratios are not exponentially commensurable. We show that the generalized finite type condition implies the weak separation property. Under this condition, we can identify the attractor of the IFS with that of a graph-directed IFS, and by modifying a setup of Mauldin and Williams [R.D. Mauldin, S.C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc. 309 (1988) 811–829], we can compute the Hausdorff dimension of the attractor in terms of the spectral radius of certain weighted incidence matrix.
Recommended Citation
Lau, Ka-Sing, Sze-Man Ngai.
2007.
"A Generalized Finite Type Condition for Iterated Function Systems."
Advances in Mathematics, 208 (2): 647-671.
doi: 10.1016/j.aim.2006.03.007
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/610
