On generalization of Sierpiński gasket in Lobachevskii plane

Abstract

© 2017, Pleiades Publishing, Ltd. We construct an analogue of Sierpiński gasket in Lobachevskii plane by means of iterated function system with maps from a transformation group of this space. The investigation of a new family of attractors and a Mandelbrot set associated with it reveals higher capacity of Lobachevskii geometry compared to that of Euclid.