finite dimensional manifold

例句：

1. 1. In thestudy of dynamical systems, finite-dimensional manifolds play a crucial role in understanding the behavior of complex systems.
   在动态系统研究中，有限维流形在理解复杂系统行为方面起着至关重要的作用。
2. 2. The theory of finite-dimensional manifolds is essential for studying the topology and geometry of differentiable manifolds.
   有限维流形理论对于研究不同光滑流形的拓扑和几何至关重要。
3. 3. The research on finite-dimensional manifolds has led to significant advances in computational geometry and numerical analysis.
   有限维流形的研究在计算几何和数值分析领域取得了显著进展。