Virtual turning points — A gift of microlocal analysis to the exact WKB analysis
Several aspects of the notion of virtual turning points are discussed; its background, its relevance to the bifurcation phenomena of a Stokes curve, its importance in the analysis of the Noumi-Yamada system (a particular higher order Painlevé equation) and a concrete recipe for locating them. Examples given here make it manifest that virtual turning points are indispensable in WKB analysis of higher order linear ordinary differential equations with a large parameter.
KeywordsTurning Point Microlocal Analysis Instanton Expansion Stokes Phenomenon High Order Linear
Unable to display preview. Download preview PDF.
- [AKKSST]T. Aoki, T. Kawai, T. Koike, S. Sasaki, S. Shudo and Y. Takei: A background story and some know-how of virtual turning points, RIMS Koukyuuroku, (ISSN 1880-2818), No.1424, 2005, pp.53–63.Google Scholar
- [CH]R. Courant and D. Hilbert: Methods of Mathematical Physics, II, Inter-science, 1962.Google Scholar
- [Ho]N. Honda: Toward the complete description of the Stokes geometry, in prep.Google Scholar
- [KT]T. Kawai and Y. Takei: Algebraic Analysis of Singular Perturbation Theory, Iwanami, Tokyo, 1998. (In Japanese; English translation, AMS, 2005)Google Scholar
- [Sa1]S. Sasaki: On the role of virtual turning points in the deformation of higher order linear ordinary differential equations, RIMS Koukyuuroku, (ISSN 1880-2818), No. 1433, 2005, pp. 27–64. (In Japanese.)Google Scholar
- [Sa2]S. Sasaki: — II — On a new Stokes curve in Noumi-Yamada system, ibid., pp. 65–109. (In Japanese.)Google Scholar
- [Sh]A. Shudo: A recipe for finding Stokes geometry in quantized Hénon map, RIMS Koukyuuroku, (ISSN 1880-2818), No. 1433, 2005, pp. 110–118.Google Scholar