文章基本信息

标题：WKB Estimates for Linear Dynamic Systems on Time Scales
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作者：Gro Hovhannisyan
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2008
卷号：2008
期号：1
页码：712913
DOI：10.1155/2008/712913
语种：English
出版社：Hindawi Publishing Corporation
摘要：We establish WKB estimates for linear dynamic systems with a small parameter 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 is based on the truncation of WKB series and WKB estimates.
关键词：Direct Calculation ; Vector Function ; Recurrence Relation ; Matrix Function ; Fundamental Matrix