Copy For Citation
AKHMET M., Alejaily E. M.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol.26, no.5, pp.2479-2497, 2021 (SCI-Expanded)
-
Publication Type:
Article / Article
-
Volume:
26
Issue:
5
-
Publication Date:
2021
-
Doi Number:
10.3934/dcdsb.2020191
-
Journal Name:
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
-
Journal Indexes:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
-
Page Numbers:
pp.2479-2497
-
Keywords:
Abstract self-similarity, self-similar space, similarity map, fractals, chaos, multi-dimensional chaotic maps, SELF-SIMILAR SETS, HAUSDORFF DIMENSION, SYSTEMS
-
Middle East Technical University Affiliated:
Yes
Abstract
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.