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Families of periodic orbits in a double-barred galaxy model. (English) Zbl 1451.85005

Summary: We reveal the networks of simple symmetric periodic orbits in a double-barred galaxy model. Specifically, we investigate the dependence on the total orbital energy of the positions but also on the stability of the periodic solutions. For every orbital family, we also compute the horizontal and vertical critical parameter values of the system, at which new periodic families bifurcate from. Of particular interest are the vertical critical points which act as starting points for the creation of new families of three-dimensional periodic orbits. The atlas of the simple periodic trajectories is presented in the \((x,E)\) plane and also in the \((x,E,z)\) and \((x,E,\dot{z})\) spaces, in order to obtain the global parametric evolution of the orbital families. Our analysis suggests that the orbital properties of a double-barred galaxy model are very complicated and at the same time very fascinating.

MSC:

85A05 Galactic and stellar dynamics
70F15 Celestial mechanics
37N05 Dynamical systems in classical and celestial mechanics
37F46 Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets
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