Chaotic property for non-autonomous iterated function system

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...

Iterated Function System Quasiarcs

We consider a class of iterated function systems (IFSs) of contracting similarities of Rn, introduced by Hutchinson, for which the invariant set possesses a natural Hölder continuous parameterization by the unit interval. When such an invariant set is homeomorphic to an interval, we give necessary conditions in terms of the similarities alone for it to possess a quasisymmetric (and as a corolla...

Generalized K-Iterated Function System

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.

Generalization of the simplest autonomous chaotic system

A New Non-Autonomous Chaotic Neural Network for Solving TSP

In this paper we propose a new chaotic noise injection strategy into the Hopfield network which belongs to a general class of chaotic neural networks called "nonautonomous network". The objective of this method is to inject noise into the neurons based on the history of dynamics of their neighbor neurons. The measure of adjacency which is a criterion for definition of neighborhood, is based on ...

Lindelöf property and the iterated continuous function spaces

We give an example of a compact space X whose iterated continuous function spaces Cp(X), CpCp(X), . . . are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul’ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces Cp(X) on compact scattered spaces with the ω1th derived set empty, improving some earlier results of Pol [12...