This article is a review and promotion of the study of solutions of differential equations in the “neighborhood of infinity” via a non traditional compactification. We define and compute critical points at infinity ...This article is a review and promotion of the study of solutions of differential equations in the “neighborhood of infinity” via a non traditional compactification. We define and compute critical points at infinity of polynomial autonomuos differential systems and develop an explicit formula for the leading asymptotic term of diverging solutions to critical points at infinity. Applications to problems of completeness and incompleteness (the existence and nonexistence respectively of global solutions) of dynamical systems are provided. In particular a quadratic competing species model and the Lorentz equations are being used as arenas where our technique is applied. The study is also relevant to the Painlevé property and to questions of integrability of dynamical systems.展开更多
目的研究谢向东,陈凤德的论文Uniqueness of limit cycles and quality of infinite criticalpoint for a class of cubic system(Ann Diff Eqs,2005,21(3):474-479)的遗留问题,是该文的继续。方法采用定性与定量的分析方法。结果完整...目的研究谢向东,陈凤德的论文Uniqueness of limit cycles and quality of infinite criticalpoint for a class of cubic system(Ann Diff Eqs,2005,21(3):474-479)的遗留问题,是该文的继续。方法采用定性与定量的分析方法。结果完整给出了系统的全局结构和分支情况。结论说明该三次系统部分全局结构和分支情况在三次系统中还是首次发现。展开更多
文摘This article is a review and promotion of the study of solutions of differential equations in the “neighborhood of infinity” via a non traditional compactification. We define and compute critical points at infinity of polynomial autonomuos differential systems and develop an explicit formula for the leading asymptotic term of diverging solutions to critical points at infinity. Applications to problems of completeness and incompleteness (the existence and nonexistence respectively of global solutions) of dynamical systems are provided. In particular a quadratic competing species model and the Lorentz equations are being used as arenas where our technique is applied. The study is also relevant to the Painlevé property and to questions of integrability of dynamical systems.
文摘目的研究谢向东,陈凤德的论文Uniqueness of limit cycles and quality of infinite criticalpoint for a class of cubic system(Ann Diff Eqs,2005,21(3):474-479)的遗留问题,是该文的继续。方法采用定性与定量的分析方法。结果完整给出了系统的全局结构和分支情况。结论说明该三次系统部分全局结构和分支情况在三次系统中还是首次发现。
