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.