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arXiv · 2211.06868

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

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.

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Hisatoshi Kodani, Kaname Matsue, Hiroyuki Ochiai, Akitoshi Takayasu. 2022-11-13. Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence. https://arxiv.org/abs/2211.06868

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