论文标题
自动ode的爆炸解决方案的多阶渐近扩展。 II-动态通信
Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence
论文作者
论文摘要
在本文中，我们提供了与平衡相关的雅各布矩阵的自然对应关系，以适当地转换了两个系统，描述了在渐进式意义上描述准综合性ODE的有限时间爆炸。作为推论，我们看到第I部分提出的爆炸的渐近扩展提供了一个标准，即在两个系统之间具有稳定信息的固有间隙结构的爆炸存在。第一部分中提供的示例进行了重审以显示上述信件。
In this paper, we provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria for appropriately transformed two systems describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic sense. As a corollary, we see that asymptotic expansions of blow-ups proposed in Part I themselves provide a criterion of the existence of blow-ups with an intrinsic gap structure of stability information among two systems. Examples provided in Part I are revisited to show the above correspondence.
