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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 = ay n -yn-1, {a :|a|<2, a≠0,±1}, y0, y1 , are periodic. The first-order system representation of this equation is shown to have self-similar and chaotic solutions in the integer plane.

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Correspondence to Dean Clark.

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Clark, D. Periodic solutions of arbitrary length in a simple integer iteration. Adv Differ Equ 2006, 035847 (2006). https://doi.org/10.1155/ADE/2006/35847

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Periodic Solution
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