A discrete chaotic dynamical system on the Sierpinski gasket

Abstract

The Sierpinski gasket (also known as the Sierpinski triangle) is one of the fundamental models of self-similarsets. There have been many studies on different features of this set in the last decades. In this paper, initially we constructa dynamical system on the Sierpinski gasket by using expanding and folding maps. We then obtain a surprising shiftmap on the code set of the Sierpinski gasket, which represents the dynamical system, and we show that this dynamicalsystem is chaotic on the code set of the Sierpinski gasket with respect to the intrinsic metric. Finally, we provide analgorithm to compute periodic points for this dynamical system.