English

Jordan curves and funnel sections

Dynamical Systems 2011-02-15 v1 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.1102.2644,
  title  = {Jordan curves and funnel sections},
  author = {Charles Pugh and Conan Wu},
  journal= {arXiv preprint arXiv:1102.2644},
  year   = {2011}
}

Comments

22 pages, 16 figures

R2 v1 2026-06-21T17:25:36.867Z