For small b the Henon map reproduces the dynamics of the quadratic map. The map equations can be rewritten
|xn+1||=||yn + 1 - axn2 + bxn-1|
This is shown for a=1.98 (which is equivalent to the value of 3.99 for the quadratic map parameter, i.e. the value giving chaos over the full unit interval) and b=0.01:
It should be noted that the curve is not strictly one dimensional - this can be seen better by enlarging the portion of the curve near the maximum - as must be the case for the invertibility of the Henon map to be preserved.