Title

Graph-Directed Iterated Function Systems Satisfying the Generalized Finite Type Condition

Document Type

Article

Publication Date

8-10-2010

Publication Title

Nonlinearity

DOI

10.1088/0951-7715/23/9/013

ISSN

1361-6544

Abstract

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.

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