Order-reducing Form Symmetries and Semiconjugate Factorizations of Difference Equations
| dc.creator | Sedaghat, H. | |
| dc.date | 2008-04-22 | |
| dc.date | 2008-05-27 | |
| dc.date.accessioned | 2026-07-07T09:40:46Z | |
| dc.date.available | 2026-07-07T09:40:46Z | |
| dc.description | The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally using the semiconjugate relation on a group which yields a reduction of order through the semiconjugate factorization of the difference equation of order $k+1$ into equations of lesser orders. Different classes of equations are considered including separable equations and homogeneous equations of degree 1. Applications include giving a complete factorization of the linear non-homogeneous difference equation of order $k+1$ into a system of $k+1$ first order linear non-homogeneous equations in which the coefficients are the eigenvalues of the higher order equation. Form symmetries are also used to explain the complicated multistable behavior of a separable, second order exponential equation. | |
| dc.description | 25 pages, 2 figures; reduction of order based on the new concept of form symmetry and semiconjugate factorization; Version 2 adds a converse to Theorem 2, a new example and several remarks; it also updates references (two new papers on this topic accepted) and corrects minor errors | |
| dc.identifier | https://arxiv.org/abs/0804.3579 | |
| dc.identifier | http://arxiv.org/abs/0804.3579 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161593 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 39A10 (Primary); 39A11, 39A20, 39B12, 39B52, 39B72 (Secondary) | |
| dc.title | Order-reducing Form Symmetries and Semiconjugate Factorizations of Difference Equations | |
| dc.type | text |