On self-affine measures and self-affine sets
by
Ka-Sing Lau
The Chinese University of Hong Kong
Coauthors: Qirong Deng and Xinggang He

Let A be an n×n expanding integral matrix and let D={d₁, ..., d_N} ⊂ Zⁿ. We discuss the self-affine measure m and the self-affine set K generated by the affine pair (A, D). Our main consideration is to reduce the involved overlapping iterated function system into a tractable graph directed system, which yields a vector-valued representation for the self-affine measure. By using this we can handle the fractal structure and calculate various dimensions of m and K.

Date received: June 12, 2006