Computational Methods and Function Theory 3 (2003), No. 1, 105--115
Copyright Heldermann Verlag 2003
J. Milne Anderson
helen@math.ucl.ac.uk, Department of Mathematics, University College London, London WC1E 6BT, U.K.
F. David Lesley
lesley@math.sdsu.edu, Department of Mathematics and Statistics, San Diego State University, San Diego CA 92182, U.S.A.
Vladimir I. Rotar
rotar@sciences.sdsu.edu, Department of Mathematics and Statistics, San Diego State University, San Diego CA 92182, U.S.A.; Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russian Federation.
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.
Keywords: Conformal mapping, boundary properties, non-rectifiable curves, Kolmogorov's Theorem, one-sided estimates Lyapunov ratio condition.
MSC 2000: 30C35, 60C05.
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