Dufraine Emmanuel
Universite de Bourgogne, Laboratoire de Topologie, U.M.R. 5584 du C.N.R.S., B.P. 47870-21078 Dijon Cedex, France.
Chaos. 2001 Sep;11(3):443-448. doi: 10.1063/1.1385918.
We deal here with vector fields on three manifolds. For a system with a homoclinic orbit to a saddle-focus point, we show that the imaginary part of the complex eigenvalues is a conjugacy invariant. We show also that the ratio of the real part of the complex eigenvalue over the real one is invariant under topological equivalence. For a system with two saddle-focus points and an orbit connecting the one-dimensional invariant manifold of those points, we compute a conjugacy invariant related to the eigenvalues of the vector field at the singularities. (c) 2001 American Institute of Physics.
我们在此研究三维流形上的向量场。对于一个具有到鞍 - 焦点的同宿轨道的系统，我们证明复特征值的虚部是一个共轭不变量。我们还证明复特征值实部与实特征值的比值在拓扑等价下是不变的。对于一个具有两个鞍 - 焦点以及连接这些点的一维不变流形的轨道的系统，我们计算了一个与奇点处向量场特征值相关的共轭不变量。（c）2001美国物理研究所。
