动力学系统可以看成是映输入空间到输出空间的一个算子，在特定时刻动力学系统的输出可以看成是其输入空间上的一个泛函，这样动力学系统建模就可以看作是表征系统映射关系的算子或泛函的逼近问题。研究了多层神经网络的非线性映射能力，给出了多层网络可一致逼近有限维空间Ｒｎ紧集上的连续函数、无穷维函数空间紧集上的连续泛函和连续算子的理论证明。得出的几个一般性结论为在动力学系统建模等领域应用神经网络准备了理论工具。 The dynamic system can be regarded as an operator mapping the input space to the output space. At certain moment, the output of the dynamic system can be regarded as a functional in the input space, so the dynamic system modeling can be regarded as Approximation Problem of Operator or Function Representation of System Mapping Relationship. The nonlinear mapping ability of multi-layer neural network is studied. The continuous function of multi-layer network can be approximated uniformly by the compact set of Rn over a finite dimensional space. The continuous functional and the theoretical proof . Several general conclusions have been drawn to prepare theoretical tools for the application of neural networks in the field of dynamic system modeling.