Factorization of Difference Equations by Semiconjugacy with Application to Non-autonomous Linear Equations
Exactly Solvable and Integrable Systems
2012-03-02 v1 Dynamical Systems
Abstract
The existence of a semiconjugate relation permits the transformation of a higher order difference equation on a group into an equivalent triangular system of two difference equations of lower orders. Introducing time-dependent form symmetries in this paper enables us to identify the semiconjugate property in a larger set of non-autonomous difference equations than previously considered. We show that there is a substantial class of equations having this feature that includes the general (non-autonomous, non-homogeneous) linear equation with variable coefficients in an arbitrary algebraic field.
Cite
@article{arxiv.1005.2428,
title = {Factorization of Difference Equations by Semiconjugacy with Application to Non-autonomous Linear Equations},
author = {Hassan Sedaghat},
journal= {arXiv preprint arXiv:1005.2428},
year = {2012}
}
Comments
The general theory of semiconjugate factorization of non-autonomous higher order difference equations, 16 pages