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

2018/06/22 by Kaname Matsue, Matsue, Kaname · 1 citation
Mathematics · Physics and Astronomy · #34A26 #34C08 #35B44 #35L67 #58K55 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Biology Tumor Growth #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1806.08487

openalex publication_date 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Numerical validation of blow-up solutions with quasi-homogeneous compactifications

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