Related papers: Dynamics Motivated by Sierpinski Fractals
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some…
The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
In complex dynamics, a fundamental result of Fatou and Julia asserts that every attracting cycle of a rational map attracts a critical point. The analogous statement fails in non-Archimedean dynamics. For a non-Archimedean rational map,…
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian…
The family of Generalised Sierpinski triangles consist of the classical Sierpinski triangle, the previously well investigated Pedal triangle and two new triangular shaped fractal objects denoted by $\triangle FNN$ and $\triangle FFN$. All…
This article constructs a fractal interpolation function, also referred to as $\alpha$-fractal function, using Suzuki-type generalized $\varphi$-contraction mappings (STGPC). The STGPC is a generalization of $\varphi$-contraction mappings.…
We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system. We allow red, green and blue light to reflect off a mirrored sphere, which is…
Recently there has been growing interest in extending the thermodynamic method from static configurations to dynamical trajectories. In this approach, ensembles of trajectories are treated in an analogous manner to ensembles of…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some contrasting behaviour of these sets as those with in case of a…
Josephson junctions (JJs) are by nature neuromorphic hardware devices capable of mimicking excitability and spiking dynamics. When coupled together or combined with other superconducting elements, they can emulate additional behaviors found…
Orbital magnetization (OM) in Sierpinski carpet (SC) and triangle (ST) fractal is theoretically investigated by using Haldane model as a prototypical example. The OM calculation is performed following two distinct approaches; employing the…
Let $f$ be a rational map with degree $d\geq 2$ whose Julia set is connected but not equal to the whole Riemann sphere. It is proved that there exists a rational map $g$ such that $g$ contains a buried Julia component on which the dynamics…
An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency,…
Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…