Delay Embedding & Takens' Theorem — Attractor Reconstruction

🌀 TAKENS DELAY EMBEDDING

Source system: Delay τ (steps): 20 Embedding dim d: 3 Trail length: 800

Left: original phase space
Right: delay-embedded x(t),x(t+τ),x(t+2τ)

Takens (1981): generic smooth embedding of attractor using delay coordinates. dim≥2d_A+1 (Whitney). Enables attractor reconstruction from single observed time series.