|
|
| |
| TIME-VARYING VECTOR FIELDS ON A COMPACT RIEMANNIAN MANIFOLD (I) |
| |
Citation： |
Lin xiaodong.TIME-VARYING VECTOR FIELDS ON A COMPACT RIEMANNIAN MANIFOLD (I)[J].Chinese Annals of Mathematics B,1988,9(1):95~106 |
| Page view： 818
Net amount： 679 |
Authors： |
Lin xiaodong; |
|
|
| Abstract： |
This paper studies critical points of a time-varying vector field $\[f:M \times R \to TM\]$ on a compact Riemannian manifold M. It is shown that if a critical point $\[{x_0}\]$ admits an exponential dichotomy, then there are two families of manifolds,stable manifold family and unstable manifold family of $f$ through $\[{x_0}\]$ in some open neighborhood $V$ of $\[{x_0}\]$, moreover , the critical point $\[{x_0}\]$ is isolated. Also it is shown that the solution curve family of the perturbed time-varying vector field yielded by a small change of $f$ is qualitatively the same as that of $f$. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
