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العنوان
On the Study of some Dynamical
Systems: Generalized Problem of Two
Fixed Center and Kovalevskaya-Yehia
Case /
المؤلف
Khalil, Salma Khalil Zakria.
هيئة الاعداد
باحث / Salma Khalil Zakria Khalil
مشرف / Fawzy Mohammed Fahmy El-Sabaa
مشرف / Mona Hosny Abd Elkhalek Ali
مناقش / Mona Hosny Abd Elkhalek Ali
تاريخ النشر
2018.
عدد الصفحات
120 p. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الرياضيات التطبيقية
تاريخ الإجازة
1/1/2018
مكان الإجازة
جامعة عين شمس - كلية التربية - قسم الرياضيات
الفهرس
Only 14 pages are availabe for public view

from 120

from 120

Abstract

The aim of this thesis is to
1- Study the topological analysis of the problems under consideration. 2- Get the periodic solution by giving the solution in terms of Jacobi’s elliptic functions.
3- Determine the singular points by using the phase portrait.
4- Use Poincare´ surface section to show that the motion is regular in the integrable cases.
The thesis consists of four chapters:
Chapter 1
The goal of this chapter is to study the topological analysis, the periodic solution and the phase portrait of the problem of two-fixed center.
The results of this chapter are:
Published in Astrophysics and Space Science, vol. 363, 2018.
Chapter 2
In chapter 2, we studied the topological analysis, the periodic solu- tion and the phase portrait of the generalized two-fixed center problem. The results of this chapter are:
Accepted in Italian Journal of Pure and Applied Mathematics, vol. 43, 2018
Chapter 3
The Purpose of this chapter studied the topological analysis, the periodic solution, the phase portrait and Poincare´ surface section of

Armbruster Guckenheimer Kim (AGK) galactic potential.
The results of this chapter are:
Published in Astrophysics and Space Science, vol. 364, 2019.
Chapter 4
Finally, in this chapter, we introduce a survey of the Kovalevskaya- Yehia problem starting when Yehia introduced a new first integral of the problem. Moreover, we get the topological type of the isoenergy surfaces of Kovalevskaya-Yehia case with g = 0.