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Geometrical construction of a chaotic horseshoe-like map on Cantor dust C×C×C

Author

Listed:
  • Koparal, Fatma Diğdem
  • Aslan, Nisa
  • Saltan, Mustafa
  • Özdemir, Yunus
  • Demir, Bünyamin

Abstract

Smale’s horseshoe map is one of the most important examples of 2D chaos in dynamical systems. Its chaotic behavior is often illustrated using a two-sided shift map. In this paper, a 3−dimensional horseshoe-like map is defined inspired by the geometrical motivation of the horseshoe map of Smale. Moreover, this construction is expressed on the Cantor dust (C×C×C) via ternary numbers and then the density of the periodic points is proved by using a different technique. To compute these periodic points more rapidly, we also give an algorithm. Finally, it is shown that this version of 3D horseshoe-like map is Devaney chaotic.

Suggested Citation

  • Koparal, Fatma Diğdem & Aslan, Nisa & Saltan, Mustafa & Özdemir, Yunus & Demir, Bünyamin, 2024. "Geometrical construction of a chaotic horseshoe-like map on Cantor dust C×C×C," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009342
    DOI: 10.1016/j.chaos.2024.115382
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