We consider infinite conformal function systems on Rd. We study the geometric structure of the limit set of such systems. Suppose this limit set intersects some l-dimensional C1-submanifold with positive Hausdorff t-dimensional measure, where 0 < l < d and t is the Hausdorff dimension of the limit set. We then show that the closure of the limit set belongs to some l-dimensional affine subspace ...

We consider the natural measures associated with a family of conformal iterated function systems satisfying the transversality condition but no separation condition. We provide the exact value of their generalised Renyi dimensions Dq for q in a certain range.

We reconsider the input–output model in the light of a new mathematical formalism, namely the so called Iterated Function Systems (IFS), that, in spite of the linearity of the structure of the system, allows a greatly complex dynamical behavior. The basic theory is presented and some analytical results are provided, together with some simulations (at least partly) based on empirical data.

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...

From any given Iterated Function System, a small set of balls that cover the fractal attractor can be simply determined. This gives a priori bounds on the region of space in which the attractor may be constructed.

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the λ-topology. This classification...

In 1969, Kannan [1] proved a new mapping which improved the Banach Contraction theorem. The purpose of this paper is to generalize the Kannan mapping and also to prove it, in space of fractals.

Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, i...

We study parabolic iterated function systems (IFS) with overlaps on the real line and measures associated with them. A Borel probability measure μ on the coding space projects into a measure ν on the limit set of the IFS. We consider families of IFS satisfying a transversality condition. In [SSU2] sufficient conditions were found for the measure ν to be absolutely continuous for Lebesgue-a.e. p...

We give a model of a robot’s finger and we use the methods of the theory of iterated function systems to study the asymptotic reachability set. We provide a technique for the approximation of the asymptotic reachable set and we show an explicit description of such a set in a particular case.