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Remarkably,  for an attractor of dimension D, the Takens embedding theorem [Lect. Notes. in Math.  vol.898 (1981) p366] indicates that for quite general intervals       there exists an  embedding dimension  
m ≤ 2D+1   and a smooth map                        such that


i.e. despite the possibly infinite dimensionality of the state space, the attractor and the dynamics on it can be captured in            for some  m  no bigger than  2D+1 !!!!