CONTRACTIVE MARKOV SYSTEMS

Contractive Markov Systems

Certain discrete-time Markov processes on locally compact metric spaces which arise from graphdirected constructions of fractal sets with place-dependent probabilities are studied. Such systems naturally extend finite Markov chains and inherit some of their properties. It is shown that the Markov operator defined by such a system has a unique invariant probability measure in the irreducible cas...

Contractive Systems with Inputs

Contraction theory provides an elegant way of analyzing the behaviors of systems subject to external inputs. Under sometimes easy to check hypotheses, systems can be shown to have the incremental stability property that all trajectories converge to a unique solution. This property is especially interesting when forcing functions are periodic (a globally attracting limit cycle results), as well ...

Locally Contractive Iterated Function Systems

An iterated function system on X R d is deened by successively iterating an i.i.d. sequence of random Lipschitz functions from X to X. This paper shows how Fn = f 1 fn may converge even in the absence of the strong contraction conditions | for instance, Lipschitz constant smaller than 1 on average | which earlier work has required. Instead, it is posited that there be a region of contraction wh...

Contractive function systems, their attractors andmetrization

In this paper we study the Hutchinson-Barnsley theory of fractals in the setting of multimetric spaces (which are sets endowed with point separating families of pseudometrics) and in the setting of topological spaces. We find natural connections between these two approaches.

Contractive Relaxation Systems and the Scalarmultidimensional Conservation