Combinatorics of linear iterated function systems with overlaps
نویسندگان
چکیده
منابع مشابه
Combinatorics of Linear Iterated Function Systems with Overlaps
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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We consider iterated function systems on the interval with random perturbation. Let Yε be uniformly distributed in [1 − ε, 1 + ε] and let fi ∈ C be contractions with fixpoints ai. We consider the iterated function system {Yεfi + ai(1− Yε)}i=1, were each of the maps are chosen with probability pi. It is shown that the invariant density is in L and the L-norm does not grow faster than 1/ √ ε, as ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2007
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/20/5/013