Jordan curves and funnel sections

Details Jordan curves and funnel sections Jordan curves and funnel sections

2011-02-13

arxiv.org/abs/1102.2644v1

Mathematics

Dynamical Systems

22 pages, 16 figures

Scientific paper

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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