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.
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Schedule a callMore From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
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