Periodic solutions of arbitrary length in a simple integer iteration

Authors

Dean S. Clark, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

2006

Abstract

We prove that all solutions to the nonlinear second-order difference equation in integers y_n+1 = ⌈ay _n ⌉-y_n-1, {a ∈ ℝ:|a|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.

Citation/Publisher Attribution

Clark, D. (2006). Periodic solutions of arbitrary length in a simple integer iteration. Advances in Difference Equations, 2006, 1-9. Article ID: 35847. doi: 10.1155/ADE/2006/35847

Available at: https://doi.org/10.1155/ADE/2006/35847

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.