|
|
| |
| ANTI-SADDLES OF A POLYNOMIAL SYSTEM |
| |
Citation： |
Ye Yanqian.ANTI-SADDLES OF A POLYNOMIAL SYSTEM[J].Chinese Annals of Mathematics B,1995,16(4):453~458 |
| Page view： 1167
Net amount： 804 |
Authors： |
Ye Yanqian; |
|
|
| Abstract： |
By using the generalized Poincar\'e index theorem it is proved
that if the $n^2$ critical points of an $n$-polynomial system
form a configuration of type
$(2n-1)-(2n-3)+(2n-5)-\cdots+(-1)^{n-1},$ and the $2n-1$ outmost
anti-saddles form the vertices of a convex $(2n-1)$-polygon, then
among these $2n-1$ anti-saddles at least one must be a node. |
Keywords： |
Polynomial system, Anti-saddle, Poincar\'e index
theorem, Equator. |
Classification： |
34C05 |
|
|
Download PDF Full-Text
|
|
|
|
