摘要
对于紧致流形M上的任意一个向量场X，定义了一个由向量场X确定的自映射fX：M→M，使得向量场X的奇异点均为fX的不动点．证明了向量场的Nielsen数是不依赖于向量场选取的量．
Let X be a vector field on compact manifold M. We define a self-mapping fx on M with respect to X, such that singular points of X are fixed points of fx.Then, we introduce Nielsen number, Reidemeister number and topological entropy of vector field X. Finally, we prove Nielsen number of vector field is a invariant for all vector fields.
出处
《应用数学》
CSCD
1998年第3期83-85,共3页
Mathematica Applicata
关键词
向量场
模映射
NIELSEN数
紧致流形
Vector field
Norm-mapping
Reidemeister number
Nielsen number
Topological entropy
