Iterated Function Systems with Overlaps and Self-Similar Measures
نویسندگان
چکیده
منابع مشابه
Iterated Function Systems with Overlaps and Self-similar Measures
The paper considers the iterated function systems of similitudes which satisfy a separation condition weaker than the open set condition, in that it allows overlaps in the iteration. Such systems include the well-known Bernoulli convolutions associated with the PV numbers, and the contractive similitudes associated with integral matrices. The latter appears frequently in wavelet analysis and th...
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Let p0, . . . , pm−1 be points in R, and let {fj}m−1 j=0 be a one-parameter family of similitudes of R: fj(x) = λx + (1− λ)pj , j = 0, . . . , m− 1, where λ ∈ (0, 1) is our parameter. Then, as is well known, there exists a unique self-similar attractor Sλ satisfying Sλ = ⋃m−1 j=0 fj(Sλ). Each x ∈ Sλ has at least one address (i1, i2, . . . ) ∈ ∏∞ 1 {0, 1, . . . ,m− 1}, i.e., limn fi1fi2 . . . fi...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2001
ISSN: 0024-6107
DOI: 10.1112/s0024610700001654