Non-autonomous conformal iterated function systems and Moran-set constructions

Rotation number and its properties for iterated function and non-autonomous systems  

The main purpose of this paper is to introduce the rotation number for non-autonomous and iterated function systems. First, we define iterated function systems and the lift of these types of systems on the unit circle. In the following, we define the rotation number and investigate the conditions of existence and uniqueness of this number for our systems. Then, the notions rotational entropy an...

Chaotic property for non-autonomous iterated function system

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

Separation conditions for conformal iterated function systems

Weextend both theweak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C1 conformal contractions on compact subsets of Rd . For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Haus...

Quantization Dimension for Conformal Iterated Function Systems

Language-Restricted Iterated Function Systems, Koch Constructions, and L-systems

1 Introduction Linear fractals can be generated using a variety of methods. This raises the question of finding equivalent methods for generating the same fractal. Several aspects of this question have been addressed in the literature. These include: A method for converting Koch constructions to equivalent iterated function systems (IFS's) [11], Methods for converting selected classes of L-syst...