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    \begin{center}Detecting strange attractors in turbulence: Takens' theorem 
and the Navier-Stokes equation
\end{center}
\begin{center}James Robinson
    \end{center}

Takens' celebrated time-delay embedding theorem allows the dynamics of a 
system to be reconstructed from a series of measurements at equally-spaced 
intervals of time. However, his original proof was only valid for generic 
dynamical systems evolving on finite-dimensional smooth manifolds. This was 
improved by Sauer, Yorke and Casdagli to apply to the attractors of 
finite-dimensional systems, but still excludes models of fluid dynamics and 
hence any application to physical turbulence. In this talk I will give an 
idea of the proof of a similar theorem for infinite-dimensional dynamical 
systems (e.g. parabolic partial differential equations).
I will also give a simple proof of a result of Yorke that any periodic orbit 
of an ordinary differential equation $\dot x=f(x)$ with $|f(x)-f(y)|\le 
L|x-y|$ must have period at least $1/L$, and a related infinite-dimensional 
result.
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