Related papers: Contracting on average iterated function systems b…
We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate…
This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
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…
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…
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 dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli…
We consider a class of iterated function systems (IFSs) of contracting similarities of $R^n$, introduced by Hutchinson, for which the invariant set possesses a natural H\"older continuous parameterization by the unit interval. When such an…
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…
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 study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
This study focuses on the topological pressure of nonautonomous iterated function systems defined on a compact metric space. We establish an inequality relating two topological pressures associated with a factor map of nonautonomous…
We consider a complete metric space $(X,d)$ and a countable number of contractive mappings on $X$, $\mathcal{F}=\{F_i:i\in\mathbb N\}$. We show the existence of a {\em smallest} invariant set (with respect to inclusion) for $\mathcal{F}$.…
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity of the functions in the IFS has been central to the theory of iterated functions systems.…
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…
We prove that the Markov operator associated to an iterated function system consisting of phi-max-contractions with probabilities has a unique invariant measure whose support is the attractor of the system.
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the…
We apply some methods and technique of complex dynamics to study the set of symmetries of attractors of holomorphic Iterated Function Systems (IFS), as well as relations between IFS sharing the same attractor.
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…
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…