A note on stable iterated function systems

A note on stable iterated function systems

Let X denote a compact metric space with metric d, and let f : X → X denote a continuous self-map on X . For any subset E of X , we let Cl(E) denote the closure of E. Following [1], we denote by { ,X} an iterated function system, or IFS, onX . That is, is a finite family { f1, . . . , fm} of continuous self-maps on X . In this paper we do not consider the case in which is an infinite family. Le...

A Note on Formal Iterated Function Systems

A Note on Invariant Sets of Iterated Function Systems

We prove that the family of all invariant sets of iterated systems of contractions R → R is a nowhere dense Fσ type subset in the space of the non-empty compact subsets of R equipped with the Hausdorff metric. An iterated function system (IFS for short) is a finite collection (T1, . . . , Tn) of weak contractions of a metric space X. By a weak contraction we mean a mapping T : X → X such that d...

On the Relation between Iterated Function Systems and Partitioned Iterated Function Systems on the Relation between Iterated Function Systems and Partitioned Iterated Function Systems on the Relation between Iterated Function Systems and Partitioned Iterated Function Systems

In this paper, we give a theoretically founded transition from Iterated Function Systems based on aane transformations to Partitioned Iterated Function Systems. We show that there are two essential steps, namely, restricting the aane transformations, and solving the evoked problem of ink dissipation. In this paper, we give a theoretically founded transition from Iterated Function Systems based ...

Discrete Iterated Function Systems

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