Conformal mapping and Hausdorff measures
نویسندگان
چکیده
منابع مشابه
Hausdorff Dimension and Conformal Measures of Feigenbaum Julia Sets
1.1. Statement of the results. One of the first questions usually asked about a fractal subset of R is whether it has the maximal possible Hausdorff dimension, n. It certainly happens if the set has positive Lebesgue measure. On the other hand, it is easy to construct fractal sets of zero measure but of dimension n. Moreover, this phenomenon is often observable for fractal sets produced by conf...
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We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the " hairiness phenomenon " , there exist many Feigenbaum Julia sets J(f) whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigen-baum Julia set, the Poincaré critical exponent δcr is equal to the hyperbolic dimension HD hyp (J(f)). Moreover, if a...
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A number of Hausdorff-based algorithms have been proposed for finding objects in images. We evaluate different measures and argue that the Hausdorff Average distance measure outperforms other variants for model detection. This method has improved robustness properties with respect to noise. We discuss the algorithms with respect to typical classes of noise, and we illustrate their relative perf...
متن کاملQuasiconformal Distortion of Hausdorff Measures
In this paper we prove that if φ : C → C is a K-quasiconformal map, 0 < t < 2, and E ⊂ C is a compact set contained in a ball B, then H(E) diam(B) ≤ C(K) ( H ′ (φ(E)) diam(φ(B))t′ ) t tK
متن کاملMeasure Theory on Hausdorff Measures
Let y = h(x) be defined for 0 < x < oo and assume values in 0 ^ y ^ + co. Let S be any linear set of points and p an arbitrary positive number. Cover S by a countable number of open intervals h , I2, • • • of lengths xx, x2 , • • • each of which is less than p, and denote by mp(S; h) the lower bound of h(xi) + h(x2) + • • • for all such coverings of S. Then m(S; h) = limp|0mp(/S; h) is called t...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1987
ISSN: 0004-2080
DOI: 10.1007/bf02384436