4
2015.
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 = ax 3 + bx 3 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.