Atıf İçin Kopyala
AKHMET M., Alejaily E. M.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, cilt.26, sa.5, ss.2479-2497, 2021 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
26
Sayı:
5
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Basım Tarihi:
2021
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Doi Numarası:
10.3934/dcdsb.2020191
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Dergi Adı:
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
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Sayfa Sayıları:
ss.2479-2497
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Anahtar Kelimeler:
Abstract self-similarity, self-similar space, similarity map, fractals, chaos, multi-dimensional chaotic maps, SELF-SIMILAR SETS, HAUSDORFF DIMENSION, SYSTEMS
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Orta Doğu Teknik Üniversitesi Adresli:
Evet
Özet
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.