Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence
Abstract
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.
Keywords
Cite
@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}
}
Comments
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