On Topological Conjugacy of Some Chaotic Dynamical Systems on the Sierpinski Gasket

Abstract

The dynamical systems on the classical fractals can naturally be obtained
with the help of their iterated function systems. In the recent years, dierent
ways have been developed to dene dynamical systems on the self similar sets. In
this paper, we give composition functions by using expanding and folding mappings
which generate the classical Sierpinski Gasket via the escape time algorithm. These
functions also indicate dynamical systems on this fractal. We express the dynamical
systems by using the code representations of the points. Then, we investigate
whether these dynamical systems are topologically conjugate (equivalent) or not.
Finally, we show that the dynamical systems are chaotic in the sense of Devaney
and then we also compute and compare the periodic points.