Asymptotic Approximations of the Stable and Unstable Manifolds of Fixed Points of a Two-dimensional Cubic Map

We find the asymptotic approximations of the stable and unstable manifolds of the saddle equilibrium solutions of the following difference equation xn+1 = a x3n + bx3n-1 + cxn + dxn-1, n = 0,1... where the parameters a, b, c and d are positive numbers and the initial conditions x-1 and x0 are arbitrary numbers. these manifolds determine completely the global dynamics of this equation