Frobenius morphism

例句：

1. 1.In the study of dynamical systems, Frobenius morphisms play a crucial role in analyzing the behavior of complex systems.
   在动态系统研究中，弗罗贝尼乌斯映射在分析复杂系统行为中起着至关重要的作用。
2. 2. The Frobenius morphism is used to map the state space of a system into its image space, which can help us better understand the dynamics of the system.
   弗罗贝尼乌斯映射用于将系统的态空间映射到其像空间，这有助于我们更好地理解系统的运动。
3. 3. The Frobenius morphism is also used to study the stability and controllability of nonlinear systems, which is an important topic inmodern control theory.
   弗罗贝尼乌斯映射还被用来研究非线性系统的稳定性和可控性，这是现代控制理论的一个重要课题。