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