共查询到18条相似文献,搜索用时 109 毫秒
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用直接计算的方法对一类Hamilton系统的两个Abel积分比值的单调性进行讨论,指出该单词性条件可由两个判定函数直接确定. 相似文献
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哈密顿函数H(x,y)=F(x)+G(y)所对应的哈密顿系统.给出了这类系统的周期解的周期为单调函数的几个充分条件,并用所得结果讨论了Volterral-Lotka系统和无阻尼、无强迫Duffing方程周期解周期的单调性. 相似文献
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一类可积非哈密顿系统的极限环个数的上界 总被引:3,自引:0,他引:3
In this paper, we consider the perturbations of two non-Hamiltonian integrable systems(1.3)μ, (4.1)μ. For the former,it is proved that the system under the polynomial perturbations hasat most f-n/2] limit cycles in the finite plane and the upper bound is sharp. The proof relies on acareful analysis of a related Abelian integral. For the latter, we obtain an estimate number of isolatedzeros of the corresponding Abelian integral. 相似文献
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赵育林 《数学物理学报(A辑)》2000,20(2):229-234
文进一步完善了文 [6]的工作 ,证明了 Abel积分I(h) =∮Γh(α βx γx2 ) ydx的零点个数上界 B(3)满足不等式 4≤B(3)≤ 6,这里 Γh是代数曲线 H(x,y) =12 y2 13x3 14 x4=h的连通闭分支 ,h∈ (- 1 / 1 2 ,0 )∪ (0 , ∞ ) 相似文献
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讨论了一类含参可积非Hamilton系统在一般二次多项式扰动下的Abel积分的零点,得出了不同参数范围下的Abel积分的零点数目的估计. 相似文献
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用直接计算的方法对文献中给出的第三类函数的一种特殊形式给出其积分比值单调性的判别条件. 相似文献
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The finite generators of Abelian integral are obtained, where Γh is a family of closed ovals defined by H(x,y)=x2+y2+ax4+bx2y2+cy4=h, h∈Σ, ac(4ac−b2)≠0, Σ=(0,h1) is the open interval on which Γh is defined, f(x,y), g(x,y) are real polynomials in x and y with degree 2n+1 (n?2). And an upper bound of the number of zeros of Abelian integral I(h) is given by its algebraic structure for a special case a>0, b=0, c=1. 相似文献
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Monotonicity of the ratio of two Abelian integrals for a class of symmetric hyperelliptic Hamiltonian systems 下载免费PDF全文
Rasool Kazemi 《Journal of Applied Analysis & Computation》2018,8(1):344-355
In this paper we study the monotonicity of the ratio of two hyperelliptic Abelian integrals $I_0(h)=\oint_{\Gamma_h}ydx$ and $I_1(h)=\oint_{\Gamma_h}xydx$ for which $\Gamma_h$ is a continuous family of periodic orbits of a Newtonian system with Hamiltonian function of the form $H(x,y)=\frac{1}{2}{y^2}\pm \Psi(x)$, where $\Psi$ is an arbitrary even function of degree six. 相似文献
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In this paper, we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n. The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1. 相似文献
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Chengzhi Li 《Journal of Differential Equations》2009,246(9):3609-3304
We construct a planar cubic system and demonstrate that it has at least 13 limit cycles. The construction is essentially based on counting the number of zeros of some Abelian integrals. 相似文献
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本文讨论一平面Hamilton系统在一般n次多项式扰动下的系统的Abel积分的零点个数估计问题,得到的结论是:该系统的Abel积分的零点个数的上界为[(3n-1)/2]。 相似文献
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弱化希尔伯特第16问题及其研究现状 总被引:2,自引:0,他引:2
V.I.Arnold多次提出如下问题:对于给定的自然数n≥2,所有n次多项式1-形式,沿一切可能的m≥3次闭代数曲线族的阿贝尔积分的孤立零点的最大个数Z(m,n)=?由Poincare-Pontryagin定理可知,当阿贝尔积分不恒为零时,A(n)=Z(n+1,n)给出n次Hamilton系统在n次多项式扰动下从原有周期环域分支出极限环的最大个数,因此Arnold把这个问题称为弱化的希尔伯特第16问题.30多年来,对此问题的研究取得了一定进展,也遇到了很大困难.本文拟对这个问题和相关研究工作做一个粗浅的介绍. 相似文献
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A linear estimation to the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one 下载免费PDF全文
Lijun Hong Xiaochun Hong Junliang Lu 《Journal of Applied Analysis & Computation》2020,10(4):1534-1544
In this paper, using the method of Picard-Fuchs equation and Riccati equation, we consider the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under arbitrary polynomial perturbations of degree $n$, and obtain that the upper bound of the number is $2\left[{(n+1)}/{2}\right]+$ $\left[{n}/{2}\right]+2$ ($n\geq 1$), which linearly depends on $n$. 相似文献