Related papers: Fractal Homeomorphism for Bi-affine Iterated Funct…
In this paper, we obtain coupled fixed point theorem for (\psi, \phi)-contractions under some generalized conditions on the real valued functions \psi and \phi defined on (0,\infinity). Also, we present a generalized version of coupled…
For two general polytopal complexes the set of face-wise affine maps between them is shown to be a polytopal complex in an algorithmic way. The resulting algorithm for the affine hom-complex is analyzed in detail. There is also a natural…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…
For a family of functionals defined on a Hilbert manifold and smoothly depending on a compact finite dimensional manifold, we give a sufficient condition on the parameter space in such a way the family bifurcate from the trivial branch.
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
A classical theorem of Hutchinson asserts that if an iterated function system acts on $\mathbb{R}^d$ by similitudes and satisfies the open set condition then it admits a unique self-similar measure with Hausdorff dimension equal to the…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
The aim of this work is to describe the set of fixed point free homeomorphisms of the plane under certain expansive conditions.
A finite family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps of a given metric space $X$ is called an iterated function system (shortly IFS). In a case of contractive selfmaps of a complete metric space is well-known that IFS has…
In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to…
In this paper, we introduce a construction of hidden variable recurrent fractal interpolation functions (HVRFIF) with four function contractivity factors. In the fractal interpolation theory, it is very important to ensure flexibility and…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
In this paper two important aspects related to Caputo fractional-order discrete variant of a class of maps defined on the complex plane, are analytically and numerically revealed: attractors symmetry-broken induced by the fractional-order…
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…
We study Non-autonomous Iterated Function Systems (NIFSs) with overlaps. A NIFS on a compact subset $X\subset\mathbb{R}^m$ is a sequence $\Phi=(\{\phi^{(j)}_{i}\}_{i\in I^{(j)}})_{j=1}^{\infty}$ of collections of uniformly contracting maps…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding…
Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…