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’...

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...

Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u ∈ G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the second author done for simple, adjoint G over the complex numbers. When G is simple and adjoint, the previous work of the second author makes our description com...

We introduce a Fourier-based harmonic analysis for a class of discrete dynamical systems which arise from Iterated Function Systems. Our starting point is the following pair of special features of these systems. (1) We assume that a measurable space X comes with a finite-to-one endomorphism r : X → X which is onto but not one-to-one. (2) In the case of affine Iterated Function Systems (IFSs) in...