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

Fatma Diğdem Koparal, Nisa Aslan, Mustafa Saltan, Yunus Özdemir and Bünyamin Demir

Chaos, Solitons & Fractals, 2024, vol. 187, issue C

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.

Keywords: Horseshoe map; Chaotic dynamical systems; Periodic points (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009342

DOI: 10.1016/j.chaos.2024.115382

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