analytic submanifold

例句：

1. 1. The study of the analytic submanifold is crucial for understanding the behavior of dynamical systems.
   研究分析子流形对于理解动力系统的行为至关重要。
2. 2.In this paper, we introduce a new method to solve the problem of finding the analytic submanifold in a given manifold.
   在本文中，我们介绍了一种新方法来解决给定流形中寻找分析子流形的问题。
3. 3. The analytic submanifold plays an important role in the study of differential equations and control theory.
   分析子流形在研究微分方程和控制理论中起着重要的作用。