A simple geometric construction of an ODE with undecidable blow-ups

2024/10/02 by Manh Khang Huynh, Huynh, Manh Khang
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mechanical Engineering and Vibrations Research #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2410.01455

openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a simple construction of an ODE on ℝⁿ where the vector field is smooth, and finite-time blow-up is equivalent to the halting problem for a universal Turing machine.

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