Abstract:The reconstruction theorem deals with dynamical systems that are given by a map T : X → X of a compact metric space X together with an observable f : X → R from X to the real line R. In 1981, by use of Whitney's embedding theorem, Takens proved that if T : M → M is a diffeomorphism on a compact smooth manifold M with dim M = d, for generic (T, f ) there is a bijection between elements x ∈ M and corresponding sequence (f T j (x)) 2d j=0 , and moreover, in 2002 Takens proved a generalized version for endomorphis… Show more
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