Linear chaos

العناوين الأخرى

الفوضى الخطية

مقدم أطروحة جامعية

Madih, Nur Samir Abd al-Jabbar

مشرف أطروحة جامعية

Naum, Adil Ghassan

الجامعة

جامعة بغداد

الكلية

كلية العلوم

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

العراق

الدرجة العلمية

دكتوراه

تاريخ الدرجة العلمية

2007

الملخص الإنجليزي

A pair (X, f) is a discrete dynamical system, if X is a topological metric space and f : X®X is a continuous map.

For xÎX, the orbit of x under f is : Orb(f, x) = { x, f(x), f 2(x), f 3(x),…, f n(x),…}. where f n = fo fo…o f is the nth iterate of f obtained by composing f with itself n times. There are several definitions of chaos that have appeared in the analysis of discrete dynamical systems, and there are several results considering these definitions.

In this thesis we look at these definitions and results when the space is a Hilbert space and the operator is a linear operator, as follows: First, we introduce those definitions of chaotic systems that are more frequently encountered in the literature, then we give a new definition of chaos, and we study the relation between these different definitions of chaos, also we discuss the topological conjugacy of chaotic operators. The second objective is to study the connection between transitivity, sensitivity to initial conditions, dense set of periodic points in nonlinear dynamics and in linear dynamics, then stronger forms of transitivity and sensitivity are shown. And we give two new dynamical concepts which are periodic operator and weak transitivity and we study its relation with chaotic linear operator. The third objective is to show that the chaotic of linear operators can be fantastically complex and that linear chaos exhibits the same beauty and complexity as nonlinear chaos.

And we characterize the linear chaos for backward shift operator. Finally, we study the so-called Hypercyclicity Criterion and its relation with chaos. In order to make the work accessible to the reader, we include some known results on chaos with details of the proofs in some cases, or proofs for results that are given in the literature without proofs.

التخصصات الرئيسية

الرياضيات

عدد الصفحات

79

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-603157