Short communications

Some properties of self-similar convex polytopes

A. V. Tetenov, I. B. Davydkin

Gorno-Altaisk State University, Gorno-Altaisk, Russia

Abstract: We show that for each semigroup $\mathrm G$ of similarities defining the self-similarity structure on a convex self-similar polytope $K$ there is an edge $A$ of $K$ such that the fixed points of homotheties $g\in G$ are dense in $A$.

Keywords: self-similar set, fractal, convex polytope, graph-directed IFS, homothety, semigroup.

UDC: 514.8, 515.12

MSC: 28A80

Received January 25, 2011, published February 14, 2011

Language: English