Periodic orbits of multiplicity higher than one in an N-body barred galaxy potential

Abstract

Aims. Periodic orbits (POs) have been exhaustively studied. On the contrary, to our knowledge, no complete and systematic study of higher-multiplicity (ℳ) POs, that is, orbits that close after more than one revolution in phase space, exists. Here, we fill this gap and also extend the standard tools used for studies of the x1 POs to studies of higher multiplicity POs. Methods. We adopted a multi-aspect approach, using surfaces of section, stability diagrams, characteristic diagrams, studies of the shapes of individual orbits, and other properties of the POs. We modified and extended the standard tools used for ℳ = 1, to ℳ > 1 cases, allowing them to use the snapshot information more fully. Our potential is more realistic than those of most previous studies, as it is obtained directly from a snapshot of a fully self-consistent, high-resolution numerical simulation. Results. We find five main pairs of PO families with ℳ = 2. Two of these bifurcate from the x1 family and are direct rotators, and one bifurcates from the x4 family and rotates retrograde. We suggest that the remaining families do not bifurcate, but form parts of bubbles. The POs of the x1 family have four-fold symmetry, while all the ℳ = 2 POs have only two-fold symmetry, with respect to either the x or the y axis. Furthermore, two orbits of the same Jacobi constant and from families of the same PO pair are mirror images of each other. Thus, by considering them together, it is possible to achieve four-fold symmetry. All results obtained here will be used in a following paper to study the effect of including ℳ orbits in the disc. We also show that a given family can include orbits of more than one multiplicity.