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 |

AbstractThe 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. |