Completely degenerate fixed point

The Jacobian of the Henon map is constant and equal to h. Therefore, when 6 > 0, the Henon map preserves orientation in the plane, whereas orientation is reversed when 6 < 0. Note also that if 6 < 1, the map contracts areas, so the product of the multipliers of any of its fixed or periodic points is less than 1 in absolute value. Hence, in this case the map cannot have completely unstable periodic orbit (only stable and saddle ones). On the contrary, when b > 1, no stable orbits can exist. When 6 = 1, the map becomes conservative. At b = 0, the Henon map degenerates into the above logistic map, and therefore one should expect some similar bifurcations of the fixed points when b is suflSciently small. 

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