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.

中文翻译：

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禁止星系模型中平面对称周期轨道的网络

我们在单个禁止星系模型中呈现平面对称周期轨道的网络。更具体地说，我们确定条形半长轴的数值如何不仅影响位置，而且影响周期解的线性稳定性。在（x，E）平面，以便能够理解总轨道能量对周期性网络的重要性。对于每个轨道族，我们还计算系统的水平和垂直临界解，新的周期性族从中解出。我们的分析表明，几个周期族包含的轨道符合x1型轨道并稳定了星系的禁止结构。此外，数值结果表明，棒的半长轴极大地影响了动力学系统的总体轨道特性。