Hausdorff dimension of the set of extreme points of a self-similar set

الأصل · EN

If the system S of contracting similitudes on R² satisfies open convex set condition, then the set F of extreme points of the convex hull 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 K is a convex polygon.