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Mathematics > Classical Analysis and ODEs

arXiv:2211.06868 (math)
[Submitted on 13 Nov 2022 (v1), last revised 30 Nov 2022 (this version, v2)]

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

Authors:Hisatoshi Kodani, Kaname Matsue, Hiroyuki Ochiai, Akitoshi Takayasu
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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.
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
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 34A26, 34D05, 34E05, 34E10, 58K55
Cite as: arXiv:2211.06868 [math.CA]
  (or arXiv:2211.06868v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2211.06868

Submission history

From: Kaname Matsue [view email]
[v1] Sun, 13 Nov 2022 10:07:33 UTC (561 KB)
[v2] Wed, 30 Nov 2022 13:53:13 UTC (561 KB)
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