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 ...

Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.

Contents Chapter 1. Introduction 7 1. Historical sketch 7 a. Homoclinic tangles 7 b. Geodesic flows 8 c. Picking up from Poincaré 8 d. Modern hyperbolic dynamics 9 e. The slowness of the initial development 9 2. Hyperbolic dynamics 10 3. Outline of this survey 10 a. Regularity 11 Chapter 2. Hyperbolic sets and stable manifolds 13 1. Definitions and examples 13 a. Hyperbolic linear maps, adapted...

Let t=t1t2⋯ be an element of the full shift with map τ on a finite alphabet symbols A and let Σ=closure{τi(t):i∈N∪{0}}. ft=ft1,∞=⋯∘ft2∘ft1 non-autonomous system over compact metric space X where ti∈A. The set Ft+={fτi(t):i∈N} is called shifted family ft. If t transitive in AN, then Ft+‾ classical IFS; otherwise, Σ subshift Ft+‾={fσ=fσ1,∞:σ∈Σ} “generalized” IFS. We show that if ft has some shado...

Significant research efforts are being devoted to Body Area Networks (BAN) due to their potential for revolutionizing healthcare practices. Energy-efficiency and communication reliability are critically important for these networks. In an experimental study with three different mote platforms, we show that changes in human body shadowing as well as those in the relative distance and orientation...