A discrete chaotic dynamical system on the Sierpinski gasket | Zendy

Mustafa Saltan | Zendy; Nisa Aslan | Zendy; Bünyamin DEMİR | Zendy

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A discrete chaotic dynamical system on the Sierpinski gasket

Author(s) -

Mustafa Saltan,

Nisa Aslan,

Bünyamin DEMİR

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1803-77

Subject(s) - sierpinski triangle , gasket , mathematics , dynamical systems theory , chaotic , dynamical system (definition) , set (abstract data type) , metric (unit) , fractal , pure mathematics , discrete mathematics , mathematical analysis , computer science , physics , artificial intelligence , quantum mechanics , economics , thermodynamics , programming language , operations management

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

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