Related papers: Attractor for minimal iterated function systems

In this work we propose a definition of an Euroattractor: an attracting invariant measure of a certain iterated functions system (IFS). An IFS is defined by specifying a set of functions, defined in subsets of R^N or in a classical phase…

Every quasi-attractor of an iterated function system (IFS) of continuous functions on a first-countable Hausdorff topological space is renderable by the probabilistic chaos game. By contrast, we prove that the backward minimality is a…

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,…

Consider two objects associated to the Iterated Function System (IFS) $\{1+\lambda z,-1+\lambda z\}$: the locus $\mathcal{M}$ of parameters $\lambda\in\mathbb{D}\setminus\{0\}$ for which the corresponding attractor is connected; and the…

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 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…

We consider iterated functions systems (IFS) on compact metric spaces and introduce the concept of target sets. Such sets have very rich dynamical properties and play a similar role as semifractals introduced by Lasota and Myjak do for…

In this paper we introduce expansive iterated function systems, ( IFS) on a compact metric space then various shadowing properties and their equivalence are considered for expansive IFS.

In this work we present iterated function systems with general measures(IFSm) formed by a set of maps $\tau_{\lambda}$ acting over a compact space $X$, for a compact space of indices, $\Lambda$. The Markov process $Z_k$ associated to the…

This paper discusses, certain algebraic, analytic, and topological results on partial iterated function systems($IFS_p$'s). Also, the article proves the Collage theorem for partial iterated function systems. Further, it provides a method to…

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…

For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.

This paper presents a sufficient condition for a continuum in $R^n$ to be embeddable in $R^n$ in such a way that its image is not an attractor of any iterated function system. An example of a continuum in $R^2$ that is not an attractor of…

We prove an extension of M. Hata's theorem [4] for planar Markov Iterated Function Systems satisfying a strong version of the Open Set Condition. More precisely, if the attractor of such a system is connected, then it is locally connected.…

This paper concerns the local connectedness of components of self-similar sets. Given an equal partition of the unit square into n*n small squares, we may choose arbitrarily two or more of them and form an iterated function system. The…

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 paper, the product of the Hausdorff metric on the product space is defined and the equivalency between the product Hausdorff metric and the Hausdorff metric on the product space is established. The finite product of the iterated…

The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a…

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…

We study the minimality of almost every orbital branch of minimal iterated function systems (IFSs). We prove that this kind of minimality holds for forward and backward minimal IFSs generated by orientation-preserving homeomorphisms of the…