Abstract The possibility for approximate basic statistical characteristics of atmospheric models using periodic trajectories (closed solutions of equations of dynamics) is considered. The possibility of this approximation is based on ideas of the theory of dynamical systems which states that, in some important particular cases (e.g., for hyperbolic systems), the periodic trajectories define the invariant system measure related to a notion of the system climate. It is shown that this approximation also is possible in the case of the atmospheric models under consideration. Moreover, the principal modes of circulation variability are implemented as clusters of periodic orbits oriented along the leading eigenvectors of dynamical operators of models linearized with respect to their mean states. The analysis of observational data shows that probably the same conclusion could also be made for the real atmospheric circulation.

中文翻译：

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简化的大气动力学模型中热带外大气环流和周期性轨迹的变化

摘要 考虑了使用周期性轨迹（动力学方程的封闭解）近似大气模型基本统计特征的可能性。这种近似的可能性基于动力系统理论的思想，该理论指出，在一些重要的特定情况下（例如，对于双曲线系统），周期性轨迹定义了与系统气候概念相关的不变系统测度。结果表明，在考虑的大气模型的情况下，这种近似也是可能的。此外，循环变化的主要模式被实现为周期轨道的集群，这些周期轨道沿着模型的动力算子的主要特征向量定向，相对于它们的平均状态线性化。