Annales Academić Scientiarum Fennicć
Mathematica
Volumen 32, 2007, 409-424

ON PLANAR SELF-SIMILAR SETS WITH A DENSE SET OF ROTATIONS

Kemal Ilgar Eroglu

University of Washington, Department of Mathematics
Box 354350, Seattle, WA 98195-4350, U.S.A.; kieroglu 'at' math.washington.edu

Abstract. We prove that if E is a planar self-similar set with similarity dimension d whose defining maps generate a dense set of rotations, then the d-dimensional Hausdorff measure of the orthogonal projection of E onto any line is zero. We also prove that the radial projection of E centered at any point in the plane also has zero d-dimensional Hausdorff measure. Then we consider a special subclass of these sets and give an upper bound for the Favard length of E(\rho) where E(\rho) denotes the \rho-neighborhood of the set E.

2000 Mathematics Subject Classification: Primary 28A80.

Key words: Self-similar, projection, Hausdorff, Favard.

Reference to this article: K.I. Eroglu: On planar self-similar sets with a dense set of rotations. Ann. Acad. Sci. Fenn. Math. 32 (2007), 409-424.

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