关于一类二次哈密尔顿系统在二次扰动下的极限环个数问题

本文研究了一类具有两个鞍点和一个中心的通用二次哈密尔顿向量场在二次扰动下的三参数开折，证明极限环的最小上界为２。     

关于Liénard方程极限环个数的唯n性问题

本文的定理1和3分别给出了方程组(dx)/(dt)=y-F(x),(dy)/(dt)=-g(x)在有限区间上至多有n个极限环和恰好有n个极限环的充分条件,它们分别推广了文[2]和文[1、3]中的结果。     

关于Liénard方程极限环个数的唯n性问题

本文的定理1和3分别给出了方程组(dx)/(dt)=y-F(x),(dy)/(dt)=-g(x)在有限区间上至多有 n 个极限环和恰好有 n 个极限环的充分条件,它们分别推广了文[2]和文[1、3]中的结果.     

NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES

We consider the class of polynomial differential equations x = -y+Pn(x,y), y = x + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. Inside this class we identify a new subclass of systems having a center at the origin. We show that this subclass contains at least two subfamilies of isochro-nous centers. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centers when we perturb them inside the class of all polynomial differential systems of the above form. In particular, we present a function whose simple zeros correspond to the limit cycles vvhich bifurcate from the periodic orbits of Hamiltonian systems.     

关于Liénard方程极限环的唯二性问题

<正> 首先证明了一个关于Lienard方程极限环的唯二性定理.本文减弱了他的定理的条件.     

A Note of a G.S. Petrov's Result About the Weadened 16th Hilbert Probelm

ＡＮｏｔｅｏｆａＧ．Ｓ．Ｐｅｔｒｏｖ’ｓＲｅｓｕｌｔＡｂｏｕｔｔｈｅＷｅａｋｅｎｅｄ１６ｔｈＨｉｌｂｅｒｔＰｒｏｂｌｅｍＬｉＢａｏｙｉ（李宝毅）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＴｉａｎｊｉｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ，３００１９３，Ｐ...     

AN ESTIMATE OF THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR CUBIC VECTOR FIELDS WITH CUSPIDAL LOOP

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｉｎｆｉｎｉｔｅｓｉｍａｌＨｉｌｂｅｒｔ－１６ｔｈｐｒｏｂｌｅｍ，ｐｏｓｅｄｂｙＶ．Ｉ．Ａｒｎｏｌｄ［１］，ｉｓｔｏｇｉｖｅａｎｅｓｔｉｍａｔｅＺ（ｍ，ｎ）ｏｆｔｈｅｎｕｍｂｅｒｏｆｚｅｒｏｓｏｆＡｂｅｌｉａｎｉｎｔｅ...     

关于方程x+μsinx+x=0在|x|≤(n+1)π上恰好存在n个极限环的定理

本文证明了微分方程x+μsinx+x=0(1)的等价方程组 d_x/dt=v,dv/dt=-x-μsinv (2)在相平面(x,v)的带域|v|≤(n+1)π上恰好存在n个极限环(n=1,2,…).本文对比(1)式更广泛的一类Lienard型方程证明了此结论.     

关于 Liénard 方程至多存在 n 个极限环的一个充分条件

<正> 本文给出交变阻尼的 Liénard 方程(?)+f(x)(?)+x=0或其等价方程组(dx)/(dt)=v,(dv)/(dt)=-x-f(x)v(dx)/(dt)=v,(dv)/(dt)=-x-f(x)v (1)至多有 n 个极限环的充分条件,附带改进了文[1]的工作.全文均设 f(x)∈C~0,并记 F(x)=integral from 0 to x f(x)dx.原方程组的等价方程组     

Linear estimate of the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics

We study the number of zeros of Abelian integrals for the quadratic centers having almost all their orbits formed by cubics, when we perturb such systems inside the class of all polynomial systems of degreen