可微映射R^2 --> R^2在无穷远处的内射性
Injectivity of differentiable maps R^2 --> R^2 at infinity
摘要：
定理1.1中给出的主要结果是定义在R^2中的圆$D$的补上的映射$X$被推广到R^2的拓扑嵌入的条件，不一定是满射。映射$X$是可微的，条件是：对于每个点上的某些$e>0,$，微分的特征值不属于实区间$(-e,\infty).$。这一结果与可微向量场在无穷远点的渐近稳定性有重要关系。
英文摘要：
The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to be just differentiable with the condition that, for some $e>0,$ at each point the eigenvalues of the differential do not belong to the real interval $(-e,\infty).$ The extension is obtained by restricting X to the complement of some larger disc. The result has important connections with the property of asymptotic stability at infinity for differentiable vector fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
