Iterated function systems make up an interesting class of stochastic processes which are useful for many types of stochastic modeling. In this paper we review and slightly generalize a contractivity condition guaranteeing uniqueness of invariant measures. Also, we examine how the invariant...

This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the...

Fractal geometry plays an important role in the contemporary science. In some sense, objects with integer dimension are partial cases of the more general realm of entities having a ragged shape and fractional dimension. Fractals of a broad class are described by deterministic iterated function...

Using nonlinear optimization techniques in fractal image compression. Fractal image compression generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Most practical as well as theoretical works in image processing and...

In this paper some new contractive operators on C([a, b]) of IFS type arebuilt. Inverse problems are introduced and studied by convex optimizationproblems. A stability result and some optimality conditions are given.

In this paper we recall inverse problems for iterated function systems and how these problems can be reduced to optimizations problems. We extend these results to IFS operators with dependent probabilities.

The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley,...

This work presents a novel method of reconstructing some relevant characteristics of exchange rate time series by the superposition of two components: a mostly deterministic one, the chaos game as expressed by the Yuan/USD exchange rate and a purely stochastic one, Gaussian white noise. We...

In this paper, we study some IFS Markov operators on set-valued measures (multimeasures). For this, we consider countable additivity with respect to the Minkowski sum of compact and convex sets and countable additivity with respect to (the Hausdorff closure of) unions of compact sets. After...