Semiconjugate Factorization and Reduction of Order in Difference Equations

Details Semiconjugate Factorization and Reduction of Order in Difference Equations Semiconjugate Factorization and Reduction of Order in Difference Equations

2009-07-22

arxiv.org/abs/0907.3951v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

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.

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