共查询到17条相似文献,搜索用时 62 毫秒
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利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的线性估计,得到了当n≥3时,上界为4[2n/3]+2[2n+1/3]+[2n+2/3]+16. 相似文献
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《数学的实践与认识》2015,(5)
利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分的零点个数估计,得出当n≥5时,上界为10[(4n+1)/3]+4[(4n)/3]+[(4n-1)/3]+13. 相似文献
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黎明 《数学的实践与认识》2008,38(15)
利用Picard-Fuchs方程,研究了一类二次可逆系统周期函数的单调性问题,获得了在首次积分曲线是亏格1时的二次可逆系统周期函数单调的结论. 相似文献
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利用Abel积分与第一、第二型完全椭圆积分,本文研究一类具有两个中心奇点的平面二次系统在n次小扰动下的Abel积分零点个数上界问题,得到了较小的上界估计. 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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本文研究了具有幂零奇点的七次Hamilton系统的Abel积分的零点个数问题.利用Picard-Fuchs方程法,得到了Abel积分I(h)=∮_(Γh)g(x,y)dx-f(x,y)dy在(0,1/4)上零点个数B(n≤3[(n-1)/4]),其中Γ_h是H(x,y)=x~4+y~4-x~8=h,h∈(0,1/4),所定义的卵形线f(x,y)=∑(1≤4i+4j+1≤n)aijx~(4i+1)y~4j)和g(x,y)=∑(1≤4i+4j+1≤n)bijx~4iy~(4j+1)是x和y的次数不超过n的多项式. 相似文献
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本文研究一类十一次Hamilton系统在n次多项式扰动下的Abelian积分的零点个数问题.利用Picard-Fuchs方程法,得到这类扰动Hamilton系统的Abelian积分的零点个数的上界(计重数). 相似文献
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Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One 下载免费PDF全文
Qiuli Yu Houmei He Yuangen Zhan Xiaochun Hong 《Journal of Nonlinear Modeling and Analysis》2024,6(1):218-227
By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n$. We obtain that the upper bound is $7[(n-3)/2]+5$ when $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$. 相似文献
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In this paper, using the method of Picard-Fuchs equation and Ric-cati equation, for a class of quadratic reversible centers of genus one, we re-search the upper bound of the number of zeros of Abelian integrals for thesystem (r10) under arbitrary polynomial perturbations of degree n. Our mainresult is that the upper bound is 21n - 24 (n ≥ 3), and the upper bound depends linearly on n. 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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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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一平面可积三次非Hamilton系统的Abel积分 总被引:4,自引:0,他引:4
本文讨论一平面可积三次非Hamilton系统在n次多项式扰动下Abel积分零点个数上确界,得到的结论是该Abel积分的零点个数的上确界为n。 相似文献
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该文研究在二次扰动下,亏格一双中心的二次可逆Lotka-Volterra系统周期环域产生极限环的个数问题.证明在二次扰动下,二次可逆Lotka-Volterra系统(rlv5)的周期环域产生极限环的个数不超过3. 相似文献