The Henon Map
The Henon map is a prototypical 2-D invertible iterated map with chaotic solutions proposed by the French astronomer Michel Henon (M. Henon, Commun. Math.
Phys. Phys. 50, 69-77 (1976)) as a simplified model of the Poincare map for the Lorenz model:
xn+1 = 1 + axn2 + byn
yn+1 = xn
Since the second equation above can be written as yn = xn-1, the Henon map can be written in terms of a single variable with two time delays:
xn+1 = 1 + axn2 + bxn-1
The parameter b is a measure of the rate of area contraction (dissipation), and the Henon map is the most general 2-D quadratic map with the property that the contraction is independent of x and y. For b = 0, the Henon map reduces to the quadratic map, which is conjugate to the logistic map. Bounded solutions exist for the Henon map over a range of a and b values, and a portion of this range (about 6%) yields chaotic solutions.
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Henon Map Correlation Dimension