WKB Estimates for 2×2 Linear Dynamic Systems on Time Scales. (3rd September 2008) - Hovhannisyan, Gro
Abstract : We establish WKB estimates for2 × 2 linear dynamic systems with a small parameterε on a time scale unifying continuous and discrete WKB method. We introduce an adiabatic invariant for2 × 2 dynamic system on a time scale, which is a generalization of adiabatic invariant of Lorentz_s pendulum. As an application we prove that the change of adiabatic invariant is vanishing asε approaches zero. This result was known before only for a continuous time scale. We show that it is true for the discrete scale only for the appropriate choice of graininess depending on a parameterε . The proof is based on the truncation of WKB series and WKB estimates.