Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation
type: Item
instance of: scholarly article
title: Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation
zbMATH Open document ID: 1074.39005
DOI: 10.1155/S108533750430607X
author: Ondřej Došlý
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37J10
zbMATH DE Number: 2163652
zbMATH Keywords: symplectic difference equation
zbMATH Keywords: oscillation
zbMATH Keywords: variational principle
zbMATH Keywords: Riccati technique
zbMATH Keywords: hyperbolic discrete Prüfer transformation
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
Recommended article: Q5487025
Recommended article: Symplectic difference systems: oscillation and spectral theory
Recommended article: Q3398803
Recommended article: Oscillation theorems for symplectic difference systems
Recommended article: Oscillation and spectral theory for symplectic difference systems with separated boundary conditions
Recommended article: Oscillation and conjugacy criteria for two-dimensional symplectic difference systems
Recommended article: A note on relative oscillation theory for symplectic difference systems with general boundary conditions
Recommended article: Weyl-Titchmarsh theory for symplectic difference systems
Recommended article: Comparison theorems for symplectic systems of difference equations
Recommended article: Q5322195
description: scientific article; zbMATH DE number 2163652