一类二次可逆亏格1中心的周期函数的单调性  

Monotonicity of periodic functions of a class of reversible quadratic genus with one center

作　　者：梁海华[1,2] 

机构地区：[1]中山大学数学与计算科学学院,广州510275 [2]广东技术师范学院计算机科学学院,广州510665

出　　处：《兰州大学学报（自然科学版）》2010年第5期84-88,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：广东省自然科学基金项目(9151008002000012)

摘　　要：研究了平面二次可逆系统(?)=-2xy,(?)=b-2-2(b-1)x+bx^2+2y^2.这类系统总是有一个中心奇点(1,0).证明了对每个b∈R,该中心的周期函数都是单调递增的.证明的方法是基于Picard-Fuchs方程.结论表明对这类亏格1中心而言,Chicone的猜测是正确的.The planar quadratic reversible systems x = -2xy, y = b - 2 - 2（b - 1）x ＋ bx2 ＋ 2y2 were studied. This family of planar quadratic reversible systems always have a center at （1, 0）. It was proved that the corresponding periodic function was monotonously increasing for each b ∈R. The idea used to prove the result was based on the Picard-Fuchs equation. Our main result shows that Chicone＇ conjecture is right in such reversible quadratic genus with one center.

关 键 词：单调性 周期函数 Picard—Fuchs方程 

分 类 号：O175.12[理学—数学]