Asymptotic Approximations of the Stable and Unstable Manifold of the Fixed Point of a Certain Rational Map by Using Functional Equations
DOI:
https://doi.org/10.5644/SJM.12.2.09Keywords:
Basin of attraction, competitive map, functional equation, monotonicity, stable manifold, unstable manifoldAbstract
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.
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