Summary:
In this PhD thesis we studied the structure of the phase space in the
neighborhood of periodic orbits of a 3D autonomous Hamiltonian system of
galactic type. A Basic problem was the visualization of the 4D surfaces of
section. In order to overcome this problem we used the method of color and
rotation (Patsis & Zachilas 1994). By this way, we studied and put in order
the different dynamical behavior in the neighborhood of periodic orbits
according to their stability (stable, simple unstable, double unstable, complex
unstable). Furthermore, we studied the dynamical phenomena like the phenomenon
of stickiness, the dynamics in the neighborhood of periodic orbits with high
order multiplicity, the Arnold Diffusion, the topology of the invariant
manifolds of the unstable periodic orbits, the structure of (KAM) invariant
tori and the Hamiltonian Hopf Bifurcation.
Keywords:
Chaos and Dynamical Systems, Hamiltonian Systems, Galactic Dynamics, Nonlinear Dynamics, Dynamical Astronomy
