The paper investigates fixed points and attractors of infinite iterated function systems in Cantor space. By means of the theory of formal languages simple examples of the non-coincidence of fixed point and attractor (closure of the fixed point) are given.

Iterated function systems with contracting functions have been widely applied in contexts relating art and science. This paper explores iterated function systems which consist of expanding linear functions. An area in the plane is divided in parts which are defined implicitly by an inverse function technique. With each part, an expanding function is associated. A coloring technique is proposed ...

Let {Si}i 1 be a weakly conformal iterated function system on R with attractor K. Let π be the canonical projection. In this paper we define a new concept called “projection pressure” Pπ φ for φ ∈ C Σ and show the variational principle about the projection pressure under AWSC. Furthermore, we check that the zero of “projection pressure” still satisfies Bowen’s equation. Using the root of Bowen’...

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

  This paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. In this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. The robust controller is designed on the basis of fractional Lyapunov stability theory. Furthermore, the effects of model uncertai...

We present a new solution concept for strategic games called comprehensive rationalizability that embodies a new version of “common cautious belief in rationality” based on a sound epistemic characterization in a universal type space. Differently from existing iterative strategy elimination procedures in the literature, it should rather be viewed as an iterative strategy demotion procedure as i...

In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times. Keywords—Telegraph operator, Elementary solution, Distribution

The usual attractor coding technique is to partition a given image into a number of non-overlapping range blocks. Each block of the partition is expressed as the contractive transformation of another part of the image. However, the non-overlapping partitioning induces blocking artifacts which is highly disturbing to human visual system. In this work, a novel coding scheme using iterated functio...