I. Henon Map

Henon map with cubic nonlinearity represents the map of the plane into itself:

x' = a + y - x - bxxx

The map demonstrates fractal attractors. The complete attractor body is shown in Fig.1 and Fig.2 at different values of parameters a and b .

Fig.1 (a = 0.8, b = - 0.995)

Fig.2 (a = 0.766, b = 0.4)

Fine structure of the attractor fragments are shown at Figs. 3-6.

Fig.3 (a = 0.8, b = - 0.9455)

Fig.4 (a = 0.8, b = - 0.9455)

Fig.5 (a = 0.8, b = - 0.9455)

Fig.6 (a = 0.8, b = - 0.9455)