On trajectories of analytic gradient vector fields on analytic manifolds

被引:1
作者
Nowel, A [1 ]
Szafraniec, Z [1 ]
机构
[1] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland
关键词
singularities; gradient vector fields;
D O I
10.12775/TMNA.2005.008
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let f: M -> R be an analytic proper function defined in a neighbourhood of a closed "regular" (for instance semi-analytic or sub-analytic) set P subset of f(-1)(y). We show that the set of non-trivial trajectories of the equation = del f(x) attracted by P has the same Cech-Alexander cohomology groups as Omega n {f < y}, where Omega is an appropriately choosen neighbourhood of P. There are also given necessary conditions for existence of a trajectory joining two closed "regular" subsets of M.
引用
收藏
页码:167 / 182
页数:16
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