On Lebesgue measure of integral self-affine sets

Details On Lebesgue measure of integral self-affine sets On Lebesgue measure of integral self-affine sets

2010-03-31

arxiv.org/abs/1003.6046v3

Mathematics

Metric Geometry

5 pages, 1 figure

Scientific paper

10.1007/s00454-010-9306-8

Let $A$ be an expanding integer $n\times n$ matrix and $D$ be a finite subset of $Z^n$. The self-affine set $T=T(A,D)$ is the unique compact set satisfying the equality $A(T)=\cup_{d\in D} (T+d)$. We present an effective algorithm to compute the Lebesgue measure of the self-affine set $T$, the measure of intersection $T\cap (T+u)$ for $u\in Z^n$, and the measure of intersection of self-affine sets $T(A,D_1)\cap T(A,D_2)$ for different sets $D_1,D_2\subset Z^n$.

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