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arXiv · 1806.08487

Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs

Kaname Matsue
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Abstract

Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and dynamics on their center-stable manifolds. In particular, we show that dynamics on center-stable manifolds of invariant sets at infinity with appropriate time-scale desingularizations as well as blowing-up of singularities characterize dynamics of blow-up solutions as well as their rigorous blow-up rates.

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Kaname Matsue. 2018-06-22. Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs. https://arxiv.org/abs/1806.08487

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