On the asymptotic behavior of xn+1=anxn/xn−1

We investigate the asymptotic behavior of solutions of a separable difference equation of the form

     

Perturbations of subalgebras of type II1 factors

In this paper we consider two von Neumann subalgebras and of a type II₁ factor . For a map φ on , we define

     

On the period five trichotomy of all positive solutions of xn+1=(p+xn−2)/xn

We study the behavior of all positive solutions of the difference equation in the title, where p is a positive real parameter and the initial conditions x₋₂,x₋₁,x₀ are positive real numbers. For all the values of the positive parameter p there exists a unique positive equilibrium x? which satisfies the equation