2008/04/22 by Hassan Sedaghat, Sedaghat, H. · 1 citation
Mathematics · Medicine · Physics and Astronomy · #39A10 (Primary) #39A11 #39A20 #39B12 #39B52 #39B72 (Secondary) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.0804.3579
openalex publication_date 2008/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The scalar difference equation xn+1=fn(xn,xn-1,...,xn-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.