The investigation of chaos conditions of some dynamical systems on the Sierpinski propeller

The aim of the present paper is to construct different dynamical systems on a fractal which is a not strictly self-similar set and examine chaos conditions on this structure. For this reason, we consider Sierpinski propeller as the main model and define composition functions by using some transformations such as expanding and folding mappings considering the structure of the fractal. Then, we express these systems by the code representations of their points. Moreover, we compute the periodic points of the dynamical systems and investigate whether they are chaotic or not. Finally, we compare these dynamical systems in the sense of topological conjugacy. •We first define a dynamical system on the Sierpinski Propeller, which is one of examples of a weakly self similar set.•Then, we give a formula to compute the periodic points of the dynamical system.•We investigate the chaos conditions for this dynamical system with the help of the intrinsic metric formula.•We also present a different dynamical system on the Sierpinski Propeller.•Finally, we compare these dynamical systems in the sense of topological conjugacy.