DIFFUSION OF CHAOTIC ORBITS IN BARRED SPIRAL GALAXIES

We study the diffusion of chaotic orbits in an N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions outside corotation support the spiral structure of the galaxy due to the phenomenon of stickiness close and along the unstable asymptotic manifolds of the unstable periodic orbits. These orbits are diffused outwards after about 13 rotations of the bar. During this time, the spiral structure is clearly visible and then it fades out gradually. The diffusion time for the majority of the chaotic orbits with initial conditions inside corotation is much longer than the age of the Universe. These orbits support mainly the outer parts of the bar. However, a part of the chaotic orbits inside corotation are diffused outwards fast and support the spiral structure.

DEGENERATE BIFURCATIONS OF RESONANT TORI IN HAMILTONIAN SYSTEMS

The twist condition is a necessary condition in integrable Hamiltonian systems and symplectic maps to obtain Poincaré–Birkhoff bifurcations under small perturbations. When this condition does not hold, topological structures other than Poincaré–Birkhoff chains arise in phase space through bifurcations of isolated periodic orbits and reconnections of asymptotic manifolds. In this paper we construct an integrable model Hamiltonian with degeneracies suitable to observe these phenomena close to nontwist resonant tori. The generation of isochronous chains and the stability of their fixed points is determined analytically and a condition for the reconnection is found. Particular examples are given, illustrating the bifurcation and reconnection scenario for several cases of degeneracy.