5 citations · 10 across the 7 of their papers we have counts for
7 papers
A randomly determined unpredictable function
Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
In this paper, we construct a new unpredictable function. Our approach is based on adapting the concept of symbolic dynamics to introduce a map on the space of infinite sequences g…
Chaos on the Multi-Dimensional Cube
Marat Akhmet, Ejaily Milad Alejaily
In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the…
Abstract Fractals
Marat Akhmet, Ejaily Milad Alejaily
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing…
Abstract Similarity, Fractals and Chaos
Marat Akhmet, Ejaily Milad Alejaily
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols…
Dynamics Motivated by Sierpinski Fractals
Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
Fatou-Julia iteration (FJI) is an effective instrument to construct fractals. Famous Julia and Mandelbrot sets are strong confirmations of this. In the present study, we use the pa…
Finding Dynamics for Fractals
Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
The famous Laplace's Demon is not only of strict physical determinism, but also related to the power of differential equations. When deterministically extended structures are taken…