Takens's theorem (original) (raw)

In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of a dynamical system. The reconstruction preserves the properties of the dynamical system that do not change under smooth coordinate changes (i.e., diffeomorphisms), but it does not preserve the geometric shape of structures in phase space. That is, there is a diffeomorphism that maps into such that the derivative of has full rank. is an embedding of the strange attractor in .