Open AccessOn topological conjugacy of some chaotic dynamical systems on the Sierpinski gasket
Author(s) -
Nisa Aslan,
Mustafa Saltan,
Bünyamin Demır
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2107317a
Subject(s) - topological conjugacy , iterated function system , dynamical systems theory , mathematics , sierpinski triangle , fractal , dynamical system (definition) , chaotic , pure mathematics , iterated function , conjugacy class , topology (electrical circuits) , mathematical analysis , combinatorics , computer science , physics , quantum mechanics , artificial intelligence
The dynamical systems on the classical fractals can naturally be obtained with the help of their iterated function systems. In the recent years, different ways have been developed to define 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.