Graph-Directed Iterated Function Systems Satisfying the Generalized Finite Type Condition
We extend the generalized finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we can compute the Hausdorff dimension of the attractor F in terms of the spectral radius of certain weighted incidence matrix. Moreover, if the Haudorff dimension of F is α, then the α-dimensional Hausdorff and packing measures of F are shown to be strictly positive. By assuming in addition that the graph is strongly connected, we show that the Hausdorff, packing, and box dimensions are equal and the α-dimensional Hausdorff and packing measures are finite.
Ngai, Sze-Man, Fei Wang, Xinhan Dong.
"Graph-Directed Iterated Function Systems Satisfying the Generalized Finite Type Condition."
Nonlinearity, 23 (9): 2333-2350.