Title of article :
ON THE NATURE OF SOLUTIONS OF THE DIFFERENCE EQUATION XN+1 = XNXN-3 - 1
Author/Authors :
KENT, C. M Department of Mathematics and Applied Mathematics - Virginia Commonwealth University - Richmond - Virginia, USA , KOSMALA, W Department of Mathematical Sciences - Appalachian State University - Boone - North Carolina, USA
Abstract :
We investigate the long-term behavior of solutions of the diffference
equation
xn+1 = xnxn-3 - 1 ; n = 0 ; 1 ; ... ;
where the initial conditions x-3 ; x-2 ; x-1 ; x0 are real numbers. In particular,
we look at the periodicity and asymptotic periodicity of solutions, as well as the
existence of unbounded solutions.
Keywords :
Boundedness , Periodicity , Asymptotic periodicity , Eventual periodicity , Invariant interval , Continued fractions
Journal title :
Astroparticle Physics
