A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map
A role of virtual turning points and new Stokes curves, that have been proposed as entirely new notions appearing only in higher-order differential equations, is studied in the Stokes geometry of the quantum Hénon map. Characteristics of the Stokes geometry in multi-steps are particularly focused on and generic bifurcation patterns of the Stokes geometry are listed up, which is intended to develop a “pruning theory of Stokes geometry”.
KeywordsChaotic System Lagrangian Manifold Classical Orbit Folding Point Stokes Phenomenon
Unable to display preview. Download preview PDF.
- [AKSST]Aoki, T., Kawai, T., Kokie, T., Sasaki, S., Shudo, A., Takei, T.: A background story and some know-how of virtual turning points. RIMS Kôkyûroku, 1424, 52–63 (2005)Google Scholar
- [AKT1]Aoki, T., Kawai, T., Takei, T.: New turning points in the exact WKB analysis for higher-order ordinary differential equations. In: Boutet de Monvel, L. (ed) Analyse algébrique des perturbationssingulières. I. Hermann, pp. 69–84 (1994)Google Scholar
- [Hon]Honda, N.: Toward the complete description of the Stokes geometry. In press.Google Scholar
- [Les]Giannoni, M.-J., Voros, A., Zinn-Justin, J. (ed): Chaos and quamtum Physics. Les Houches Summer School, Session LII, North-Holland, Amsterdam (1989).Google Scholar
- [S1]Shudo, A.: A recipe for finding Stokes geomtry in the quantized Hénon map. RIMS Kôkyûroku, 1433, 110–119 (2005)Google Scholar
- [S2]Shudo, A.: Stokes geometry for the quantized Hénon map. RIMS Kôkyûroku, 1424, 184–199 (2005)Google Scholar
- [S3]Shudo, A.: Stokes geometry for the quantized Hénon map in the horseshoe regime. RIMS Kôkyûroku, 1431, 107–115 (2005)Google Scholar
- [SI3]Shudo, A., Ikeda, K.S.: to be submitted.Google Scholar