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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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李伟固 《数学年刊B辑(英文版)》1990,(3)
This paper gives a necessary and sufficient condition on the existence and uniquenessof 2π-periodic solution of Duffing equation d~2x/dt~2+g(x)=p(t) (=P(t+2π)). 相似文献
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证明了关于双曲不动点的横截同宿轨意味着马蹄的Birkhoff-Smale定理对于鞍结不动点也成立. 相似文献
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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. 相似文献
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In this paper, we systematically use the idea of embedding a single diffeomor-phism into a family of diffeomorphisms (i.e., a differential flow) to discuss sometopics for one dimensional differentiable dynamical systems. 相似文献
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NotatianM a compact,boundaryless,orientable or non—orientable two-dimensional manifold of class C~∞H~r(M) the Banach space of C~r(r≥1)vector fields on M∑~r(M) the set of structurally stable vector fields in H~r(M)MS~r(M) the set of Morse—Smale vector fields in H~r(M) 相似文献
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Linear estimate of the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics 总被引:8,自引:0,他引:8
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 相似文献
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