自治常微分方程爆破解的多阶渐近展开. II -- 动力学对应
经典分析与常微分方程
2022-12-01 v2
摘要
在本文中，我们为两个适当变换的系统在渐近意义下描述具有拟齐次性的常微分方程有限时间爆破所对应的平衡态的雅可比矩阵特征结构提供了一种自然的对应。作为推论，我们看到第一部分提出的爆破渐近展开本身为两个系统间具有稳定性信息内在间隙结构的爆破的存在性提供了一个判据。我们重访了第一部分中给出的例子以展示上述对应。
引用
@article{arxiv.2211.06868,
title = {Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence},
author = {Hisatoshi Kodani and Kaname Matsue and Hiroyuki Ochiai and Akitoshi Takayasu},
journal= {arXiv preprint arXiv:2211.06868},
year = {2022}
}
备注
51 pages. This is the first part in the present subject. Part I entitled "Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I - Method and Justification" is also uploaded (arXiv:2211.06865). In v2, several expressions are unified