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The investigation of chaos conditions of some dynamical systems on the Sierpinski propeller

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  • Aslan, Nisa
  • Şeker, Saliha
  • Saltan, Mustafa

Abstract

The aim of the present paper is to construct different dynamical systems on a fractal which is a not strictly self-similar set and examine chaos conditions on this structure. For this reason, we consider Sierpinski propeller as the main model and define composition functions by using some transformations such as expanding and folding mappings considering the structure of the fractal. Then, we express these systems by the code representations of their points. Moreover, we compute the periodic points of the dynamical systems and investigate whether they are chaotic or not. Finally, we compare these dynamical systems in the sense of topological conjugacy.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003332
    DOI: 10.1016/j.chaos.2022.112123
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Rasool, Masrat & Belhaouari, Samir Brahim, 2023. "From Collatz Conjecture to chaos and hash function," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Canbaz, Beyrul, 2022. "Chaos classification in forced fermionic instanton solutions by the Generalized Alignment Index (GALI) and the largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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