Geodesic
On topological conjugacy of some chaotic dynamical systems on the Sierpinski gasket
Filomat, Tome 35 (2021) no. 7, p. 2317

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DOI

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
DOI : 10.2298/FIL2107317A
Classification : 28A80, 37D45
Keywords: Sierpinski gasket, code representation, intrinsic metric, chaotic dynamical systems, topological conjugacy 
Nisa Aslan; Mustafa Saltan; Bünyamin Demir. On topological conjugacy of some chaotic dynamical systems on the Sierpinski gasket. Filomat, Tome 35 (2021) no. 7, p. 2317 . doi: 10.2298/FIL2107317A
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     title = {On topological conjugacy of some chaotic dynamical systems on the {Sierpinski} gasket},
     journal = {Filomat},
     pages = {2317 },
     year = {2021},
     volume = {35},
     number = {7},
     doi = {10.2298/FIL2107317A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2107317A/}
}
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