In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric X , there is a Cantor set C such that the disjoint union of C and X is an attractor. In the process, it is proved that every such X is the Lipschitz image of a Cantor set.

We study a stochastic, discrete-time, economy-environment integrated model, where human activity affects the evolution of pollution over time. We assume that exogenous i.i.d. environmental shocks determine the rate of pollution transfer. We show that the pollution to capital ratio dynamics can be read as an iterated function system converging to an invariant distribution supported on a (asymmet...

A generating IFS of a Cantor set F is an IFS whose attractor is F . For a given Cantor set such as the middle-3rd Cantor set we consider the set of its generating IFSs. We examine the existence of a minimal generating IFS, i.e. every other generating IFS of F is an iterating of that IFS. We also study the structures of the semi-group of homogeneous generating IFSs of a Cantor set F in R under t...

We present a rigorous construction and generalization of the multifractal decomposition for Moran fractals with intinite product measure. The generalization is specilied by a system of nonnegative weights in the partition sum. All the usual (smooth) properties of thef(a) theory are recovered for the case that the weights are equal to unity. The generalized spectrum, !(a, r~), is invariant to a ...

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 iterated function system H. We prove that under certain assumptions on F and G, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.

We study a stochastic, discrete-time, two-sector growth model á-la Solow (1956) characterized by perpetual growth. Assuming that exogenous i.i.d. shocks hit the physical production sector, we show that the capital dynamics can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a Cantor set.

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description ...

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...

We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they ar...