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arXiv · 1905.02198

Abstract Similarity, Fractals and Chaos

Marat Akhmet·Ejaily Milad Alejaily
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Abstract

To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski fractals, Koch curve as well as Cantor set satisfy the definition. A similarity map is introduced and the problem of chaos presence for the sets is solved by considering the dynamics of the map. This is true for Poincare, Li-Yorke and Devaney chaos, even in multi-dimensional cases. Original numerical simulations which illustrate the results are delivered.

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Marat Akhmet, Ejaily Milad Alejaily. 2019-05-05. Abstract Similarity, Fractals and Chaos. https://arxiv.org/abs/1905.02198

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