On the dynamics of unit circle maps

العناوين الأخرى

ديناميكية الدوال على دائرة الوحدة

مقدم أطروحة جامعية

al-Maali, Husayn Jabir Abd al-Husayn

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

2006

الملخص الإنجليزي

Let be the unit circle defined by, and be a continuous map from into itself.

1 S {( , ) : 1} 1 2 2 S = x y ∈ R × R x + y = 1 1 f : S → S 1 S We study the dynamical properties of maps of the circle, limit set, recurrent points ,non- wandering points.

Also we study the connection between transitivity, total transitivity, mixing, sensitivity to initial conditions (SDIC).

We show that any transitive map of the circle is total transitive, and a transitive map with periodic points is SDIC.

We characterize the strong transitivity, strictly turbulent maps of the circle and we generalize some results of the interval map to maps of the circle.

We study in this work three types of chaos on circle maps (Devaney chaos, LY-chaos and ω -chaos) , we give new relation between them.

Finally, we show that a strictly turbulent map of the circle and Devaney chaos subset are equivalent, i.e.

strictly turbulent ⇔ Devaney chaos subset, and strictly turbulent implies LY-chaos but the converse is not true.

The relation between ω -chaos and strictly turbulent maps is(strictly turbulent⇔ ω -chaos).

In order to make the work accessible to the reader, we include some known results on circle maps with details of the proofs in some cases, or proofs for results that are given in the literature without proofs.

التخصصات الرئيسية

الرياضيات

الموضوعات

عدد الصفحات

95

قائمة المحتويات

Table of contents.

Abstract.

Abstract in Arabic.

Introduction.

Chapter One : Preliminaries.

Chapter Two : Relation between transitivity, mixing, sensitivity.

Chapter Three : Three types of chaos on the circle and relation between them.

References.

نمط استشهاد جمعية علماء النفس الأمريكية (APA)

al-Maali, Husayn Jabir Abd al-Husayn. (2006). On the dynamics of unit circle maps. (Doctoral dissertations Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-602986

نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)

al-Maali, Husayn Jabir Abd al-Husayn. On the dynamics of unit circle maps. (Doctoral dissertations Theses and Dissertations Master). University of Baghdad. (2006).
https://search.emarefa.net/detail/BIM-602986

نمط استشهاد الجمعية الطبية الأمريكية (AMA)

al-Maali, Husayn Jabir Abd al-Husayn. (2006). On the dynamics of unit circle maps. (Doctoral dissertations Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-602986

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-602986