Period four stability and multistability domains for the Hénon map

We report the exact analytical expression of the surface W4(a,b;λ)=0 defining stability domains for period-4 motions in the Hénon map, valid for arbitrary eigenvalues λ and parameters a and b. For λ=+1 (fold bifurcations) the expression reproduces all previous results and gives a new one. For λ=−1 (flip bifurcations) it gives analytically the missing boundary needed for the rigorous delimitation of all period-4 stability domains and for the investigation of the arithmetic nature of parameters and trajectories.