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Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
Difference equations cluster algebras Poisson bracket for integrable difference equations
2011/2/28
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Li-ouville equation, from the view point of the general T-s...
Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
2011/3/4
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
Oscillation of Second Order Nonlinear Delay Damped Difference Equations
oscillation second-order difference equations Riccati techniques
2007/12/11
Some new oscillation criteria for nonlinear delay difference equation with damping $$ \Delta ^{2}x_{n}+p_{n}\Delta x_{n}+F(n,x_{n-\tau },\Delta x_{n-\sigma })=0,\ \ \ \ n=0,1,2,\ldots ,\eqno{(*)} $$ a...