Advances in Difference Equations
Volume 2006 (2006), Article ID 35847, 9 pages
doi:10.1155/ADE/2006/35847

Periodic solutions of arbitrary length in a simple integer iteration

Abstract

We prove that all solutions to the nonlinear second-order difference equation in integers yn+1=⌈ayn⌉−yn−1,{a∈ℝ:|a|<2,a≠0,±1},y0,y1∈ℤ, are periodic. The first-order system representation of this equation is shown to have self-similar and chaotic solutions in the integer plane.