| 2x b | J = | | ij | 1 0 |has eigenvalues λ1,2 = x +- (x2 + b)1/2. Therefore for a = 1.4 and b = 0.3 the fixed point x2 = y2 = -0.883896 is unstable with λ1 = 0.1559 and λ2 = -1.9237 . The 1st figure to the left below shows the results of successive iterations of the Henon map for a = -1.4 and b = 0.3 starting from the fixed point x2 (marked by the x label). Similarly obtained plots starting with other initial values are almost identical (exept for an initial transient), suggesting that the figures is an attractor. The next figures are successive blow-ups of the squared regions in the preceding figure. Scale invariant, Cantor-set-like structura transverse to the linear structure is evident. Thus the attractor is strange with dimension between one and two.
 M.Henon "A two-dimensional mapping with a strange attractor" Comm.Math.Phys. 50, 69 (1976).