布劳威尔关于向量分布的研究

Brouwer's Research on Vector Distribution

布劳威尔通过将球面不动点定理和向量场联系起来,推动了布劳威尔不动点定理的产生,也促进了代数拓扑学的发展。基于相关原始文献,围绕布劳威尔关于向量分布的研究,分析布劳威尔对庞加莱指数工作的推广,及其对二维布劳威尔不动点定理新证明方法的思想演变过程,以期厘清布劳威尔将庞加莱的指数工作应用于一般连续向量分布的过程,及二维不动点定理新证明的具体思想。

Brouwer promoted his fixed point theorem and the development of algebraic topology by linking the two topics of spherical fixed point theorems and vector fields.Base on the related original literature and focused on Brouwer's research on vector distributions,Brouwer's generalization of Poincaré's work on exponent and the process of evolution of the idea of the new proof method of Brouwer's fixed point theorem in two dimensions were analyzed,and hence to clarify that Brouwer had applied Poincaré's work on exponent to the general process of continuous vector distributions,and provide a new proof of his fixed point theorem in two dimensions and give the specific proof idea of it.