Similarity between Henon attractor and logistic map? I noticed that layering Henon attractor images with avalue=1 and bvalues from -0.2 to 0.3 looks like  a distorted version of the logistic map.
In the image below you can see the layered images (left).
After that I tried to accentuate the first "branches" (right)

Is there any way to explain this similarity?

Henon gives the canonical definition for the map named in his honor in a 1976 publication in Communications in mathematical physics:
$$x_{n+1} = y_n +1 - a*x_n^2 \\
y_{n+1} = b*x_n$$
Substituting, we get $x_{n+1} = b*x_{n-1} + 1 - a*x_n^2$. If $b = 0$, we have $x_{n+1} = 1 - a*x_n^2$, which is just a quadratic map, of which the best known case is the logistic map. The Feigenbaum stuff is important and general, but in this case, the logistic map is simply embedded within the action of the Henon map.
