Date of Original Version
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.
Bekteševic, J., Kulenović, M. R. S., & Pilav, E. (2015). Asymptotic Approximations of the Stable and Unstable Manifolds of Fixed Points of a Two-dimensional Cubic Map. International Journal of Difference Equations, 10(1), 39-58.
Available at: http://campus.mst.edu/ijde/contents/v10n1p3.pdf