A Study of some Dynamical Systems Hénon-Heiles (H-H) and Kovalevskaya’s Top
Alshimaa Abdelbasit Mohamed Abdelhady;
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 elliptic
functions.
3- Determine the singular points by using the phase portrait.
4- Use Poincar e surface section to show that the motion is regular in the
integrable cases.
5- Use the Painlev e property to show the identi cation of speci c 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 bifurcations
of Liouville tori are determined theoretically, and the
phase portrait of separation functions of (GHH), the classi cation
of the singular points are found and we get Poincar e surface
section of the problem.
The results of this chapter are
Accepted in Italian Journal of Pure and Applied Mathematics,
2018
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 elliptic
functions.
3- Determine the singular points by using the phase portrait.
4- Use Poincar e surface section to show that the motion is regular in the
integrable cases.
5- Use the Painlev e property to show the identi cation of speci c 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 bifurcations
of Liouville tori are determined theoretically, and the
phase portrait of separation functions of (GHH), the classi cation
of the singular points are found and we get Poincar e surface
section of the problem.
The results of this chapter are
Accepted in Italian Journal of Pure and Applied Mathematics,
2018
Other data
| Title | A Study of some Dynamical Systems Hénon-Heiles (H-H) and Kovalevskaya’s Top | Other Titles | دراسة بعض الأنظمة الديناميكية: إينو – هايلز ونحلة كافيلفسكيا | Authors | Alshimaa Abdelbasit Mohamed Abdelhady | Issue Date | 2019 |
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