Example (2-D Quadratic Iterated Map)

xn+1 = a1 + a2xn + a3xn2 + a4xnyn + a5yn + a6yn2

yn+1 = a7 + a8xn + a9xn2 + a10xnyn + a11yn + a12yn2

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Equivalence (diffeomorphism) between systems with:

1 variable with many time delays

Multiple variables and no delay

Takens' theorem (1981)

A generalization of the Mandelbrot set equations