Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials

Abstract

We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral galaxies. These potentials are known for providing building blocks to support observed features such as the peanut, or X-shaped bulge, in the former case and the spiral arms in the latter. We investigate the possibility that these structures are reinforced, apart by regular orbits, also by orbits in the vicinity of complex unstable periodic orbits. We examine the evolution of the phase space structure in the immediate neighbourhood of the periodic orbits in cases where the stability of a family presents a successive transition from stability to complex instability and then to stability again, as energy increases. We find that we have a gradual reshaping of invariant structures close to the transition points and we trace this evolution in both models. We conclude that for time scales significant for the dynamics of galaxies, there are weakly chaotic orbits associated with complex unstable periodic orbits, which should be considered as structure-supporting, since they reinforce the morphological features we study.

21 pages, 16 figures (accepted for publication in Physica D: Nonlinear Phenomena)

References in corpus (6)

• Dawes Review 4: Spiral Structures in Disc Galaxies
• The phase-space of boxy-peanut and X-shaped bulges in galaxies I. Properties of non-periodic orbits
• Partially chaotic orbits in a perturbed cubic force model
• Dynamics of thick, open spirals in Perlas potentials
• Geometry of complex instability and escape in four-dimensional symplectic maps
• Chaotic orbits obeying one isolating integral in a four dimensional map