Networks of planar symmetric periodic orbits in a barred galaxy model

Abstract

We present the networks of planar symmetric periodic orbits in a single barred galaxy model. More specifically, we determine how the numerical value of the bar's semimajor axis affects not only the positions but also the linear stability of the periodic solutions. The atlas of the periodic orbits, with multiplicity up to 10, is presented on the (x, E) plane so as to be able to understand the importance of the total orbital energy on the periodic networks. For every orbital family, we also compute the horizontal and vertical critical solutions of the system, from which new periodic families bifurcate. Our analysis indicates that several periodic families contain orbits, which qualify as x1 type orbits and stabilize the barred structure of the galaxy. Furthermore, the numerical results suggest that the semimajor axis of the bar highly influences the overall orbital properties of the dynamical system.