Hausdorff dimension of the set of extreme points of a self-similar set
Abstract
Description
If the system S of contracting similitudes on $ R^2$ satisfies open convex set condition, then the set F of extreme points of the convex hull $\tilde{K}$ of it's invariant self-similar set K has Hausdorff dimension 0 .
If, additionally, all the rotation angles of the similitudes are commensurable with $π$, then the set F is finite and the convex hull $\tilde{K}$ is a convex polygon.
10 pages, 3 figures, Latex2e
10 pages, 3 figures, Latex2e