A 2-D example (Hénon map)

2

b

-2

a

-4

1

xn+1 = 1 + axn2 + bxn-1

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Simplest 2-D chaotic system

Two control parameters

Reduces to logistic map for b = 0

Chaotic "beach" on NW side of "island" occupies about 6% of area

Does probability of chaos decrease with dimension?