周期函数的高阶导数
The period functions' higher order derivatives
摘要：
本文证明了平面微分系统周期环中周期函数$T$的$n$阶导数的一个公式。对于$n = 1$，得到了周期一阶导数\cite{FGG}的Freire，Gasull和Guillamon公式.我们把这样的结果应用到变量可分的哈密顿系统和其它系统。给出了周期函数为守恒二阶O.D. E的若干充分条件。是凸的
英文摘要：
We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order O.D.E.'s to be convex.
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