Displaying similar documents to “Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation.”

Phases of linear difference equations and symplectic systems

Zuzana Došlá, Denisa Škrabáková (2003)

Mathematica Bohemica

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The second order linear difference equation Δ ( r k ▵ x k ) + c k x k + 1 = 0 , ( 1 ) where r k ≠ 0 and k ∈ ℤ , is considered as a special type of symplectic systems. The concept of the phase for symplectic systems is introduced as the discrete analogy of the Borůvka concept of the phase for second order linear differential equations. Oscillation and nonoscillation of (1) and of symplectic systems are investigated in connection with phases and trigonometric systems. Some applications to summation of number series are given, too. ...