扭转弯曲定理和它的一个应用

The Twist-bend Theorem With an Application

本文对解析映射证明了一个不动点定理(称为扭转弯曲定理),其中弯曲条件取代了经典扭转定理(参考Ding W.Y.,A generalization of the Poincare-Birkhoff theorem,Proc.Amer.Soc.,1983,88:341-346)中的保面积条件;然后用本文的扭转弯曲定理证明了一类耗散的Duffing方程拥有高阶的次调和解.

In this paper,a fixed-point theorem（called twist-bent theorem） is proved for analytic maps,where the bend condition replaces the area-preserving condition in the classic twist theorem（see the Reference（Ding W.Y.,A generalization of the Poincare-Birkhoff theorem, Proc.Amer.Soc,1983,88：341-346））.Then the twist-bend theorem is applied to proving the existence of subharmonic solutions of certain dissipative Duffing equation containing small parameters.