Related papers: Equicontractive weak separation property on the li…
This paper aims at formulating definitions of topological stability, structural stability, and expansiveness property for an iterated function system( abbrev, IFS). It is going to show that the shadowing property is necessary condition for…
It has been shown that certain 2-vertex directed graph iterated function systems (IFSs), defined on the unit interval and satisfying the convex strong separation condition (CSSC), have attractors whose components are not standard IFS…
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…
A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1…
An infinite iterated function system (IIFS) is a countable collection of contraction maps on a compact metric space. In this paper we study the conditions under which the attractor of a such system admits a parameterization by a continuous…
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension.…
In this paper we will introduce the methodology of analysis of the convex hull of the attractors of iterated functional systems (IFS) - compact fixed sets of self-similarity mapping. The method is based on a function which for a direction,…
A sequence of points $z_k$ in the unit disk is said to be thin for a given decrease function $\rho$, if there is a nontrivial bounded holomorphic function such that the infinite series $\sum_k \rho(1-|z_k|)|f(z_k)|$ converges. All sequences…
We study weakly hyperbolic iterated function systems on compact spaces, as defined by Edalat, but in the more general setting of a compact parameter space. We prove the existence of attractors, both in the topological and measure…
Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane have uniformly perfect attractor sets, while other conditions imply the attractor is pointwise thin, and thus…
For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.
Until recently, it was an important open problem in Fractal Geometry to determine whether there exists an iterated function system acting on $\mathbb{R}$ with no exact overlaps for which cylinders are super-exponentially close at all small…
For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation…
We consider convex sets and functions over idempotent semifields, like the max-plus semifield. We show that if $K$ is a conditionally complete idempotent semifield, with completion $\bar{K}$, a convex function $K^n\to\bar{K}$ which is lower…
If $F$ and $G$ are iterated function systems, then any infinite word $W$ in the symbols $F$ and $G$ induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single $C^{1 + \alpha}$…
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
We investigate whether the Hutchinson operator associated with the iterated function system (IFS) is continuous. It clarifies several partial results scattered across recent literature. While the main example for IFS with strict attractor…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…