ASYMPTOTIC APPROXIMATIONS OF THE STABLE AND UNSTABLE MANIFOLD OF THE FIXED POINT OF A CERTAIN RATIONAL MAP BY USING FUNCTIONAL EQUATIONS | Zendy

M. R. S. Kulenović | Zendy; E. Pilav | Zendy

Open Access

ASYMPTOTIC APPROXIMATIONS OF THE STABLE AND UNSTABLE MANIFOLD OF THE FIXED POINT OF A CERTAIN RATIONAL MAP BY USING FUNCTIONAL EQUATIONS

Author(s) -

M. R. S. Kulenović,

E. Pilav

Publication year - 2016

Publication title -

sarajevo journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 2233-1964

pISSN - 1840-0655

DOI - 10.5644/sjm.12.2.09

Subject(s) - mathematics , manifold (fluid mechanics) , point (geometry) , stable manifold , fixed point , mathematical analysis , pure mathematics , geometry , mechanical engineering , engineering

We find an asymptotic approximations of the stable and unstable manifolds of the saddle equilibrium solution and the periodtwo solutions of the following difference equation xn+1 = p + xn−1/xn, where the parameter p is positive number and the initial conditions x −1 and x0 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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