Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence

Autor:	Kodani, Hisatoshi, Matsue, Kaname, Ochiai, Hiroyuki, Takayasu, Akitoshi
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs 34A26 34D05 34E05 34E10 58K55
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.06868 Zobrazit plný text záznamu View this record from Arxiv