Recover strange attractor topology from a 1D time series · delay embedding · mutual information
Delay Embedding: x(t) vs x(t+τ)
Takens 1981: generically, delay embedding
reconstructs attractor up to diffeomorphism.
m ≥ 2d+1 sufficient (d = attractor dim)
Mutual Information & False Neighbors
Optimal τ: first minimum of I(τ)
Optimal m: FNN fraction drops to ~0