Asymptotic Approximations of the Stable and Unstable Manifold of the Fixed Point of a Certain Rational Map by Using Functional Equations - Kulenović, M.R.S.; Pilav, E. (Sarajevo Journal of Mathematics, 2024)
Dedicated to the memory of Professor Mahmut Bajraktarevi´c We find an asymptotic approximations of the stable and unstable manifolds of the saddle equilibrium solution and the period-two solutions of the following difference equation x_n+1 = p+x_n-1/x_n, where the parameter p is positive number and the initial conditions x_-1 and x_0 are positive numbers. These manifolds, which satisfy the standard functional equations of stable and unstable manifolds determine completely global dynamics of this equation.