相关论文: On the continuity of the Hutchinson operator
We consider iterated function systems $\mathrm{IFS}(T_1,\dots,T_k)$ consisting of continuous self maps of a compact metric space $X$. We introduce the subset $S_{\mathrm{t}}$ of {\emph{weakly hyperbolic sequences}} $\xi=\xi_0\ldots\xi_n…
In $T_1$ compact topological spaces the Hutchinson operator of a contractive IFS (iterated function system; a finite family of closed mappings from the space into itself) may not be closed. Nevertheless, the Hutchinson operator of a…
We associate to each iterated function system consisting of phi-max-contractions an operator (on the space of continuous functions from the shift space on the metric space corresponding to the system) having a unique fixed point whose image…
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 study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are…
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…
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…
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…
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.…
In the present work, we study the attractors of iterated function systems (IFSs) on connected and compact metric spaces. We prove that the whole of the phase space of a forward minimal IFS, for which some map admits an attracting fixed…
Given an iterated function system (IFS) on a complete and separable metric space $Y$, there exists a unique compact subset $X \subseteq Y$ satisfying a fixed point relation with respect to the IFS. This subset is called the attractor set,…
In the paper we unify two extensions of the classical Hutchinson--Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuzzy IFS) on a Tychonoff space $X$ which is contracting w.r.t.…
We introduce the novel concept of hypercomplex iterated function system (IFS) on the complete metric space $(\mathbb{A}_{n+1}^k,d)$ and define its hypercomplex attractor. Systems of hypercomplex function systems arising from hypercomplex…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
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…
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…
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.…
This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem…
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.
One of the easiest and common ways of generating fractal sets in ${\mathbb R}^D$ is as attractors of affine iterated function systems (IFS). The classic theory of IFS's requires that they are made with contractive functions. In this paper,…