Jordan curves and funnel sections

2011/02/13 by Charles Pugh, Pugh, Charles, Conan Wu +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1102.2644

openalex publication_date 2011/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the case when solution of an ODE at a given initial condition fail to be unique and investigate what are the possible time-1 sections of the `solution funnel'. Along the way we give construction of a natural complete metric on the space of Jordan curves and prove that the generic Jordan curve is nowhere pierceable by arcs of finite length.

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