Related papers: Weak Shadowing Property for IFS
Iterated function systems (IFS) provide a powerful method for constructing fractals and modeling complex structures. This paper develops the notion of a dynamical system of IFS to study how an initial IFS evolves over time. We construct a…
We introduce a general approach to characterize composite fading models based on inverse gamma (IG) shadowing. We first determine to what extent the IG distribution is an adequate choice for modeling shadow fading, by means of a…
In 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of shadowing, average shadowing, transitive,…
We investigate the topological and metric properties of attractors of an iterated function system (IFS) whose functions may not be contractive. We focus, in particular, on invertible IFSs of finitely many maps on a compact metric space. We…
We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map $f$ of a compact metric space has the limit shadowing property, then the restriction of $f$ to the non-wandering…
This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability…
In the present paper, we define the concept of weak topological conjugacy and we establish sufficient conditions to obtain this kind of topological conjugacy between two limit sets. We use the character of recurrence to obtain the results.
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces.…
In this paper, for iterated function systems, we define the classic concept of the dynamical systems: topological conjugacy of diffeomorphisms. We generalize the Hartman-Grobman theorem for one dimensional iterated function systems on R.…
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated function system (IFS) corresponding to the data set is the graph of the FIF. Coalescence…
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in $\br^d$, and the ``IFS'' refers to…
We consider low-dimensional systems with the shadowing property. In dimension two, we show that the shadowing property for a homeomorphism implies the existence of periodic orbits in every $\epsilon$-transitive class, and in contrast we…
For an iterated function system (IFS) of simillitidues, we define two graphs on the representing symbolic space. We show that if the self-similar set $K$ has positive Lebesgue measure or the IFS satisfies the weak separation condition, then…
We provide an overview of iterated function systems (IFS), where randomly chosen state-to-state maps are applied iteratively to a state. We aim to summarize the state of art and, where possible, identify fundamental challenges and…
In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of the functions, but we do not assume any separation condition.…
We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…
We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W…
We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…
We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…