English

Semiconjugate Factorization and Reduction of Order in Difference Equations

Exactly Solvable and Integrable Systems 2012-03-27 v1 Dynamical Systems

Abstract

We discuss a general method by which a higher order difference equation on a group is transformed into an equivalent triangular system of two difference equations of lower orders. This breakdown into lower order equations is based on the existence of a semiconjugate relation between the unfolding map of the difference equation and a lower dimensional mapping that unfolds a lower order difference equation. Substantial classes of difference equations are shown to possess this property and for these types of equations reductions of order are obtained. In some cases a complete semiconjugate factorization into a triangular system of first order equations is possible.

Keywords

Cite

@article{arxiv.0907.3951,
  title  = {Semiconjugate Factorization and Reduction of Order in Difference Equations},
  author = {H. Sedaghat},
  journal= {arXiv preprint arXiv:0907.3951},
  year   = {2012}
}

Comments

Reduction of order of difference equations by semiconjugate factorization is formally explained. 28 pages, 2 figures

R2 v1 2026-06-21T13:28:00.316Z