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We investigate the evolution of phase space close to complex unstableperiodic orbits in two galactic type potentials. They represent characteristicmorphological types of disc galaxies, namely barred and normal (non-barred)spiral galaxies. These potentials are known for providing building blocks tosupport observed features such as the peanut, or X-shaped bulge, in the formercase and the spiral arms in the latter. We investigate the possibility thatthese structures are reinforced, apart by regular orbits, also by orbits in thevicinity of complex unstable periodic orbits. We examine the evolution of thephase space structure in the immediate neighbourhood of the periodic orbits incases where the stability of a family presents a successive transition fromstability to complex instability and then to stability again, as energyincreases. We find that we have a gradual reshaping of invariant structuresclose to the transition points and we trace this evolution in both models. Weconclude that for time scales significant for the dynamics of galaxies, thereare weakly chaotic orbits associated with complex unstable periodic orbits,which should be considered as structure-supporting, since they reinforce themorphological features we study.

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