Abstract:Let A be an n × n real expanding matrix and D be a finite subset of R n with 0 ∈ D. The family of maps {f d (x) = A −1 (x + d)} d∈D is called a self-affine iterated function system (self-affine IFS). The self-affine set K = K(A, D) is the unique compact set determined by (A, D) satisfying the set-valued equation K = d∈D f d (K). The number s = n ln(#D)/ ln(q) with q = | det(A)|, is the so-called pseudo similarity dimension of K. As shown by He and Lau, one can associate with A and any number s ≥ 0 a natural ps… Show more
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