一类通有二次哈密顿系统的环性(英文)

1 IntroductionConsider the fOllowing system:t'here E is a small parameter, H(I, y) is a polynomial of degree (n + 1 ) ? f(I, y)and g(x, y) are polynomials of degree S n. The corresponding Abelian integrallswhere b(h) is a compact leve1 curve H--'(h) of (1.l) when E = 0, for h lyingbetween criticaI values of H. The Hilbert-Arnold prob1em (weakend Hilbert16th problern) is to find an upper boulld of the nurnber of zeros of (l.2) forfixed n 2 2 and for al1 H, f and g. In this paper, we tvi11…     

PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

ＰＥＲＩＯＤＩＣＯＲＢＩＴＳＩＮＰＥＲＴＵＲＢＥＤＧＥＮＥＲＡＬＩＺＥＤＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳＺｈａｏＸｉａｏｈｕａ（赵晓华）Ｄｅｐｔ．ｏｆＭａｔｈ．ｏｆＹｕｎｎａｎＵｎｌｙ．＆Ｉｕｓｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．ｏｆＹｕｎｎａｎＰｒｏｖ...     

HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS

The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+▽V(t,q(t))=0,where V(t,x)=-K(t,x)+W(t,x),K(t,x) is neither a quadratic form in x nor periodic in t and W(t,x) is superquadratic in x.     

INFINITELY MANY HOMOCLINIC ORBITS FOR A CLASS OF HAMILTONIAN SYSTEMS WITH SYMMETRY

§１．ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓＴｈｉｓｐａｐｅｒｉｓａｎｅｘｔｅｎｓｉｏｎｏｆｔｈｅｗｏｒｋ［８］．Ｗｅｃｏｎｓｉｄｅｒｔｈｅｅｘｉｓｔｅｎｃｅｏｆｉｎｆｉｎｉｔｅｌｙｍａｎｙｈｏｍｏｃｌｉｎｉｃｏｒｂｉｔｓｆｏｒｔｈｅｆ...     

HOMOCLINIC ORBITS FOR A CLASS OF HAMILTONIAN SYSTEMS WITH POTENTIALS CHANGING SIGN

In this paper, we prove the existence of nontrivial homoclinic orbits for a class of Hamiltonian systems with potential changing sign. We use Mountain Pass Lemma.     

MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANAR HAMILTONIAN SYSTEM

In this paper, Melnikov functions which apper in the study of limit cycles of a perturbed planar Hamiltonlan system are studied. There are two main contributions here. The first one is related to the explicit formulae for these functions: a new method is developed to achieve the goal for the second one (Theorem A). the authors also discover a close relation between Melnlkov functions and focal qtmntities (Theorem 13). This relation is useful in both judging when a Melnikov function is identically zero and simplifying the computation of a Melnikov function (see §5). I)espite these results, this paper also includes other related resuEs, e.g. some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system.     

HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

ＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＳＩＮＰＥＲＴＵＲＢＥＤＧＥＮＥＲＡＬＩＺＥＤＨＡＭＩＬＴＯＮＩＡＮ　ＳＹＳＴＥＭＳ￥ＺｈａｏＸｉａｏｈｕａ（赵晓华）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＯｆＹｕｎｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋｕｎｍｉｎｇ６５０００１，Ｃｈｉｎａ...     

一列Liouville可积的有限维Hamilton系统族

本文直接递归地生成了一列Liouville可积的有限维Hamilton系统族，给出了其一串对合的公共运动积分和一组对合的生成元．     

一类带阻尼项的次二次二阶Hamilton系统的周期解

本文研究了一类带阻尼项的二阶Hamilton系统周期解的存在性问题.利用鞍点定理,在新的次二次条件下,获得了一个新的存在性结果,推广并改进了已有文献的相关存在性结论.     

LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS

In this paper,we are concerned with a cubic near-Hamiltonian system,whose unperturbed system is quadratic and has a symmetric homoclinic loop.By using the method developed in [12],we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop.Further,we give a condition under which there exist 4 limit cycles.     

一类无穷维Hamilton算子的谱刻画及其可逆性

研究了定义域为对角形的上三角无穷维Hamilton算子:H=的谱刻画及其可逆性;当A的剩余谱不含关于虚轴对称的点时,H的谱等于A的谱与A的谱关于虚轴对称分支的并集,并得到了H的预解集为空及其可逆的充要条件;作为结论的应用,得到当A为无穷维Hamilton算子时,H的点谱、剩余谱、连续谱和谱分别等于A的点谱、剩余谱、连续谱和谱.     

周期系数的平面Hamilton系统的平衡解的稳定性

本文考虑周期系数的平面Hamilton系统H(x,y,t)=H2(x,y,t)+H4(x,y,t)+d(x,y,t)的平衡解的稳定性。其中H2(x,y,t)=1/2[a(t)x2+y2],H4(x,y,t)=b4(t)x4+b2(t)(xy)2+b0(t)y4以及a(t),b0(t),b2(t),b4(t)是连续的T-周期函数,d(x,y,t)关于时间也是T-周期,在原点附近其阶为(x2+y2)3.     

一类Hamilton系统周期映射的单调性

本文证明了系统 x+α· x+β· xn=0 (α>0 ,β≠ 0 ,n 2 )的周期映射是单调的     

PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEA RHAMILTONIAN SYSTEMS

ＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡＳＹＭＰＴＯＴＩＣＡＬＬＹＬＩＮＥＡＲＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳＦｅｉＧｕｉｈｕａＱｉｕＱｉｎｇｊｉｕＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＤｅｃｅｍｂｅｒ５，１９９４．ＲｅｖｉｓｅｄＳｅｐｔｅ...     

THE EXISTENCE OF HOMOCLINIC ORBITS FOR HAMILTONIAN SYSTEMS WITH THE POTENTIALS CHANGING SIGN

§1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　　ＷｅｃｏｎｓｉｄｅｒｔｈｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ¨ｑ-Ｌ(ｔ)ｑ Ｖ′(ｔ,ｑ)=0,(ＨＳ)ｗｈｅｒｅ(ｔ,ｑ)∈Ｒ×ＲＮ,¨ｑ=ｄ2ｄｔ2ｑ,Ｖ′(ｔ,ｑ)ｄｅｎｏｔｅｓｔｈｅｇｒａｄｉｅｎｔｏｆＶ(ｔ,ｑ)ｗｉｔｈｒｅｓｐｅｃｔｔｏｑ,ａｎｄｔｈｅｓｙｍｍｅｔｒｉｃｍａｔｒｉｘＬ(ｔ)ｉｓａｓｓｕｍｅｄｔｏｓａｔｉｓｆｙ:(Ｌ)Ｌ(ｔ)∈Ｃ(Ｒ,ＲＮ2)ａｎｄｔｈｅｒｅｅｘｉｓｔｓλ>0ｓｕｃｈｔｈａｔＬ(ｔ)ｘ·ｘλ｜ｘ｜2,(ｔ,ｘ)∈Ｒ×ＲＮ.Ｗｅａｓｓｕｍ…     

对称群上的一类Cayley图的边传递性和Hamilton性

Let Sn be the symmetric group,g+I=(123i),g-I=(1i32) and M+n={g+I:4≤I≤n},then M+n is a minimal generating set of Sn,where n≥5.It is proved that Cayley graph Cay(Sn,M+n∪M-n) is Hamiltonian and edge symmetric.     

一族可积Hamilton方程

本文利用屠规彰格式,导出了一族新的可积系,包含４个未知函数,具有双Ｈａｍｉｌｔｏｎ结构,且以ＴＣ族为特例。     

THE TRACE INDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS （III）

§1.ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｈｅｏｒｙｏｆｉｎｔｅｇｒａｂｌｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｏｆｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎｓｈａｓｕｎｄｅｒｇｏｎｅａｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｓｉｎｃｅｔｈｅｌａｔｅ1960’ｓ(ｓｅｅａｓｈｏｒｔｓｕｒｖｅｙｉｎ[1]ａｎｄｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ).ＢｏｔｈｔｈｅｆｉｎｉｔｅａｎｄｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｉｎｔｅｇｒａｂｌｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｈａｖｅｂｒｏａｄａｐｐｌｉｃａｔｉｏｎｓｉｎｖａｒｉｏｕ…     

ON TWO CONJECTURES OF THE QUADRATIC DIFFERENTIAL SYSTEMS

ＯＮＴＷＯＣＯＮＪＥＣＴＵＲＥＳＯＦＴＨＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＺＨＡＮＧＸＩＡＮＧ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＳｅｐｔｅｍｂｅｒ２９，１９９５．＊ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃ...