العنوان A Study of some Dynamical Systems Hénon-Heiles (H-H) and Kovalevskaya’s Top / المؤلف Alshimaa Abdelbasit Mohamed Abdelhady هيئة الاعداد باحث / الشيماء عبدالباسط محمد عبدالهادي مشرف / فوزي محمد فهمي السبع مشرف / منى حسني عبدالخالق علي تاريخ النشر 2019. عدد الصفحات 156 p. : اللغة الإنجليزية الدرجة ماجستير التخصص الرياضيات التطبيقية تاريخ الإجازة 1/1/2019 مكان الإجازة جامعة عين شمس - كلية التربية - رياضيات تطبيقية الفهرس | Only 14 pages are availabe for public view |

AbstractThe aim of this thesis is to 1- Study the topological analysis of the mentioned problems in this thesis. 2- Get the periodic solution by giving the solution in terms of Jacobi’s ellip- tic functions. 3- Determine the singular points by using the phase portrait. 4- Use Poincar´ e s urface section to show that the motion is regular in the integrable cases. 5- Use the Painlev´ e p roperty to show the identification of specific integrable cases. This thesis consists of two parts: • Part one consists of - Chapter 1 We studied a complete description of the real phase topology of a generalized H`enon-Heiles System (GHH), and all generic bi- furcations of Liouville tori are determined theoretically, and the phase portrait of separation functions of (GHH), the classifica- tion of the singular points are found and we get Poincar´ e s urface section of the problem. The results of this chapter are Accepted in Italian Journal of Pure and Applied Mathematics, 2018. Chapter 2 We introduce a new integrable case of Yang-Mills problem [46] by using Painlev´ e p roperty. A complete description of the real phase topology of Yang-Mills galactic potential is introduced and studied. Moreover, all generic bifurcations of Liouville tori are determined theoretically and the periodic solution is presented, and the phase portrait and the Poincar´ e s urface-section are stud- ied. Part two consists of - Chapter 3 The goal of this chapter is to study the phase portrait, the classification of singular points, the bifurcation diagram for the problem, and the numerical calculation by using Poincar´ e s urface section of the case of Kovalevskaya. The results of this chapter are Published in journal of Applied Mathematics and Physics, V. 5, 2017. |