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Dynamical analysis of some special shift maps on discrete Sierpinski triangle

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  • Seyhan, Özlem
  • Aslan, Nisa
  • Saltan, Mustafa

Abstract

There is a natural relationship between fractals and chaos. In addition, different chaotic dynamical systems can be defined depending on the structure of the relevant fractal. In this paper, we first define a family of dynamical systems on the discrete Sierpinski triangle by using the composition of the shift map and the elements of S3, which is the group of symmetries of the equilateral triangle, via the code representations of the points. Moreover, we give a general formula to construct different dynamical systems on this fractal. Thus, we obtain a family of dynamical systems which are Devaney chaotic. Finally, we classify these dynamical systems in term of topological conjugacy.

Suggested Citation

  • Seyhan, Özlem & Aslan, Nisa & Saltan, Mustafa, 2024. "Dynamical analysis of some special shift maps on discrete Sierpinski triangle," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012845
    DOI: 10.1016/j.chaos.2023.114382
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    References listed on IDEAS

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    1. Valle, João & Machicao, Jeaneth & Bruno, Odemir M., 2022. "Chaotical PRNG based on composition of logistic and tent maps using deep-zoom," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Aslan, Nisa & Şeker, Saliha & Saltan, Mustafa, 2022. "The investigation of chaos conditions of some dynamical systems on the Sierpinski propeller," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Aslan, Nisa & Saltan, Mustafa & Demir, Bünyamin, 2019. "The intrinsic metric formula and a chaotic dynamical system on the code set of the Sierpinski tetrahedron," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 422-428.
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