We propose a semianalytical method for the calculation of widths, libration centers and small amplitude libration periods of the mean motion resonances k_p:k in the framework of the circular restricted three body problem valid for arbitrary eccentricities and inclinations. Applying the model to the trans Neptunian region (TNR) we obtain several atlas of resonances between 30 and 100 au showing their domain in the plane (a,e) for different orbital inclinations. The resonance width may change substantially when varying the argument of the perihelion of the resonant object and in order to take into account these variations we introduce the concept of resonance fragility. Resonances 1:k and 2:k are the widest, strongest, most isolated ones and with lower fragility for all interval of inclinations and eccentricities. We discuss about the existence of high k_p:k resonances. We analyze the distribution of the resonant populations inside resonances 1:1, 2:3, 3:5, 4:7, 1:2 and 2:5. We found that the populations are in general located near the regions of the space (e,i) where the resonances are wider and less fragile with the notable exception of the population inside the resonance 4:7 and in a lesser extent the population inside 3:5 which are shifted to lower eccentricities.

中文翻译：

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海王星外平均运动共振的三维结构

我们提出了一种半解析方法，用于在圆形受限三体问题的框架内计算平均运动共振 k_p:k 的宽度、振动中心和小振幅振动周期，适用于任意偏心率和倾斜度。将该模型应用于跨海王星区域 (TNR)，我们获得了几个 30 到 100 天文单位之间的共振图谱，显示了它们在平面 (a,e) 中不同轨道倾角的域。当改变共振物体的近日点自角时，共振宽度可能会发生很大变化，为了考虑到这些变化，我们引入了共振脆性的概念。共振 1:k 和 2:k 是最宽、最强、最孤立的共振，并且对于所有倾斜和偏心区间的脆弱性较低。我们讨论高 k_p:k 共振的存在。我们分析了共振 1:1、2:3、3:5、4:7、1:2 和 2:5 内共振种群的分布。我们发现种群通常位于空间 (e,i) 的区域附近，在这些区域共振更宽且不那么脆弱，除了共振 4:7 内的种群以及在较小程度上 3 内的种群之外:5 转移到较低的偏心率。