Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation (Q1773508)

The author describes a variational principle, the Riccati technique and several transformation methods for the investigation of oscillatory properties of the symplectic difference equation \[ z_{k+1} = \mathcal{S}_k z_k, \;k = 0,1,\dots, \] where \(z \in \mathbb{R}^{2n}, \;\mathcal{S}_k^T J \mathcal{S}_k = J, \;\mathcal{S}_k \in \mathbb{R}^{2n \times 2n},\) \(J = \bigl( \begin{matrix} 0 & I \\ -I & 0 \end{matrix}\bigr).\) A so-called hyperbolic discrete Prüfer transformation is proposed.