Dynamical study of Henon-Heiles Hamiltonian system

Abstract

This thesis deals with one of the most important and popular dynamical systems—the H´enon-Heiles Hamiltonian system—and the calculation of the critical points, stabilities, instabilities, chaos, and bifurcations of the system. In addition, we demonstrate different types of orbits (periodic, chaotic, and regular) and some of the island types of the system by using the Poincar´e sur face of sections with different E values. Furthermore, we clarify the changes in the graph shape of the system as the time period changes (the system ap pears clearer when the time period is bigger) and as the dimension changes (two-dimensional in contrast to three-dimensional).