Semiconjugate Factorization and Reduction of Order in Difference Equations

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.

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

References in corpus (1)

• Order-reducing Form Symmetries and Semiconjugate Factorizations of Difference Equations

Cited by in corpus (2)

• Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
• Reduction of Order, Periodicity and Boundedness in Nonlinear, Higher Order Difference Equations