WKB Estimates for Linear Dynamic Systems on Time Scales

WKB Estimates for Linear Dynamic Systems on Time Scales

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We establish WKB estimates for linear dynamic systems with a small parameter bible flask on a time scale unifying continuous and discrete WKB method.We introduce an adiabatic invariant for 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 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.The proof safavieh couture furniture is based on the truncation of WKB series and WKB estimates.