ABSTRACT SIMILARITY, FRACTALS AND CHAOS


AKHMET M. , Alejaily E. M.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, cilt.26, sa.5, ss.2479-2497, 2021 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 26 Konu: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3934/dcdsb.2020191
  • Dergi Adı: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
  • Sayfa Sayıları: ss.2479-2497

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.