Abstract similarity, fractals and chaos

2021-05-01
A new mathematical concept of abstract similarity is introduced and is illustrated in the space of infinite strings on a finite number of symbols. The problem of chaos presence for the Sierpinski fractals, Koch curve, as well as Cantor set is solved by considering a natural similarity map. This is accomplished for Poincare, Li-Yorke and Devaney chaos, including multi-dimensional cases. Original numerical simulations illustrating the results are presented.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

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Citation Formats
M. Akhmet, “Abstract similarity, fractals and chaos,” DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, pp. 2479–2497, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/89471.