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Abstract similarity, fractals and chaos
Date
2021-05-01
Author
Akhmet, Marat
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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.
URI
https://hdl.handle.net/11511/89471
Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
DOI
https://doi.org/10.3934/dcdsb.2020191
Collections
Department of Mathematics, Article
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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.