hnon map

The Hnon map is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hnon map takes a point

(x,y)

of the plane and maps it to a new point

f_{a,b}(x,y) = (y+1-a x^2, b x)

The map depends on two constants

a

and

b

, which have the canonical values of

a = 1.4

and

b = 0.3

The map was introduced by Michele Hnon as a simplified model of the Poincar section of the Lorenz model. For the canonical map (a=1.4 and b=0.3) an initial point of the plane will either approach a set of points known as the Hnon strange attractor, or will diverge to infinity. The Hnon attractor is a fractal, smooth in one direction and a Cantor set in another. As a dynamical system, the canonical Hnon map is interesting because, unlike the logistic map, its orbits defy a simple description.

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