Systems on Time Scales
نویسنده
چکیده
We establish WKB estimates for 2 × 2 linear dynamic systems with a small parameter ε on a time scale unifying continuous and discrete WKB method. We introduce an adiabatic invariant for 2 × 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 as ε 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 parameter ε. The proof is based on the truncation of WKB series and WKB estimates.
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