论文标题:亚纯函数的线性组合与一类代数体函数的亏量
Deficiencies of Linear Combination of Meromorphic Function and a Class of Algebrodial Function
论文作者 张积林
论文导师 吴桂荣,论文学位 硕士,论文专业 基础数学
论文单位 福建师范大学,点击次数 75,论文页数 39页File Size599k
2002-04-01论文网 http://www.lw23.com/lunwen_90886162/ 亚纯函数;代数体函数;亏量关系
quadratic system,homoclinic cycle,global phase graphs
本文基于Wronskian行列式的定义及有关性质，主要讨论了一类亚纯函数线性组合的亏量关系。得到代数体函数亏量的某些结果。在本文第一节中给出Wronskian行列式的定义及有关性质。第二节中将仪洪勋与杨重骏在1995年证明的关于亚纯函数的线性组合的亏量关系以及K．NIINO-OZAWA的相关结果推广到较一般的情形。第三节中运用K．NIINO-OZAWA的方法建立了由方程Ψ(z，w)=W~n+A_(n-1)(z)W~(n-1)+…+A_o(z)=0所确定的代数体函数，当A_i(z)(j=0，1，2，…n-1)为亚纯函数时，H．Cartan恒等式仍成立。并证明了在这个条件下代数体函数亏量关系的某些结果，推广了K．NIINO与M．OZAWA在文献[1]中的一个定理，同时指出了文献[1]中定理2.29证明的欠妥之处并加以改正。
So far it is still difficult to determine the homoclinic (or heteroclinic)bifurcation in the quadratic systems and there are many reminded questiones about the algebraic solvable part of this problem. This thesis devotes to study the homoclinics of quadratic systems and their revelent problems.The content is divided to four parts.In the first part, the generic quadratic systems with a hyperbolic saddle are discussed. By transforming the systems to a certain normal form, we obtain some necessary conditions for the systems possessing the homoclinic cycle.In the second part, we discuss two kinds of integrable systems with a hyperbolic saddle. One is symmetric integrable system,the other is hamiltonian integrable system.We analysis in detail the conditions of the systems possessing homoclinic cycles,then give all of the complete bifurcation curves in the parameter plane and the global phase graphs of the systems.In the third part,we study the question of parameter unfolding of a simple hamiltonian system.By choosing the proper parameters, we can get a four-dimension parameter domain which ensures the unfolded system have the limit cycle .The boundaries of the domains corresponding to poincdre, homoclinic, het-eroclinic, hopf or saddle-node bifurcation of the systems.Finally,we present a kind of quintic curve whose non-isolated component can constitute the homoclinic cycle of the quadratic systems.
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