الفهرس 
On generalized Henon-Heiles of the galactic potentialOnly 14 pages are availabe for public view
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Abstract
The 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.