On a Dyadic Parametrization of Curves

被引：0
|
作者：
J. Milne Anderson
F. David Lesley
Vladimir I. Rotar
机构：
[1] University College London,Department of Mathematics
[2] San Diego State University,Department of Mathematics and Statistics
[3] Russian Academy of Sciences,Central Economics and Mathematics Institute
来源：
Computational Methods and Function Theory | 2004年 / 3卷 / 1期
关键词：
Conformal mapping; boundary properties; non-rectifiable curves; Kolmogorov’s Theorem; one-sided estimates Lyapunov ratio condition.; 30C35; 60C05;
D O I：
10.1007/BF03321028
中图分类号：
学科分类号：
摘要：
A “dyadic parametrization” of a (presumably non-rectifiable) curve in the complex plane is introduced, along with the notions of a dyadic tangent and a dyadic twist point. The parametrization of a curve leads to a tree of angles, to which we apply some theorems on probability. Using one sided inequalities of Paley Zygmund type, we find conditions for the set of points with dyadic tangents and the set of twist pionts to have Hausdorff dimension one.
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页码：105 / 115
页数：10
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