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