On the geometry of a Riemann surface underlying a virtual turning point

• Project/Area Number: 20540150
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: HONDA Naofumi Hokkaido University, 大学院・理学研究院, 准教授 (00238817)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: WKB解析 / 完全WKB解析 / 漸近解析 / ストークス幾何 / 代数解析

Research Abstract

We study the geometry underlying a virtual turning point, which appears in exact WKB analysis. For this purpose, we have constructed a Riemann surface associated with a linear differential equation with a large parameter and a depth function which indicates dependency between new Stokes curves. As an application, we show that we can really obtain connection coefficients on all the new Stokes curves.

Research Products

• [Journal Article] Stratified Whitney jets and tempered ultradistributions on the subanalytic site (2011)
  • Author(s): Naofumi Honda, Giovanni Moranndo
  • Journal Title: Bulletin de la Societe Mathematique de France in press
  • Peer Reviewed
• [Journal Article] Multi-specialization and multi-asymptotic expansion (2011)
  • Author(s): Naofumi Honda, Luca Prelli
  • Journal Title: Proceedings of the Japan Academy 87 Pages: 69-72
  • NAID: 120006459687
  • Peer Reviewed
• [Journal Article] On the number of the turning points of the second kind of the Noumi Yamada system (2011)
  • Author(s): Takashi Aoki, Naofumi Honda, Yoko Umeta
  • Journal Title: RIMS Kokyuroku Bessatsu in press
  • Peer Reviewed
• [Journal Article] Multi-specialization and multi-asymptotic expansions (2011)
  • Author(s): Naofumi Honda, Luca Prelli
  • Journal Title: Proc.Japan.Acad. Volume: 87, A
  • NAID: 120006459687
  • Peer Reviewed
• [Journal Article] Geometric properties of the Riemann surface associated with the Noumi-Yamada system with a large parameter (2011)
  • Author(s): Takashi Aoki, Naofumi Honda
  • Journal Title: Journal of Mathematical Society of Japan Volume: Accepted
  • NAID: 10030344748
  • Peer Reviewed
• [Journal Article] Stratified Whitney jets and tempered ultradistributions on the subanalytic site (2010)
  • Author(s): N.Honda, G, Morando
  • Journal Title: Bulltetin de la Societe Mathematique de France Accepted
  • Peer Reviewed
• [Journal Article] On the number of the turning points of the second kind of the Noumi-Yamada systems with a large parameter (2010)
  • Author(s): T.Aoki, N.Honda, Y.Umeta
  • Journal Title: RIMS Koukyuroku Bessatsu Accepted
  • Peer Reviewed
• [Journal Article] The geometric structure of a virtual turning point and the model of the Stokes geometry (2009)
  • Author(s): Naofumi Honda
  • Journal Title: RIMS Kokyuroku Bessatsu B10 Pages: 63-117
  • Peer Reviewed
• [Journal Article] The geometric structure of a virtual turning point and the model of the Stokes geometry (2009)
  • Author(s): N.Honda
  • Journal Title: RIMS Koukyuroku Bessatsu B10 Pages: 63-113
  • Peer Reviewed
• [Journal Article] Principally tame regular sequences associated with the forth Painleve hierarchy with a large parameter (2008)
  • Author(s): Takashi Aoki, Naofumi Honda
  • Journal Title: Proceedings of the Japan Academy 84 Pages: 42-47
  • Peer Reviewed
• [Journal Article] The no-response approach and its relation to non-interactive methods for the inverse scattering (2008)
  • Author(s): Naofumi Honda, Gen Nakamura, R.Potthast, Murad Sini
  • Journal Title: Ann Math.Pura Appl. 187 Pages: 188-215
  • Peer Reviewed
• [Journal Article] The geometric structure of a virtual turning point and the model of the Stokes geometry (2008)
  • Author(s): N.Honda
  • Journal Title: RIMS Kokvuroku Bessatsu B10 Pages: 63-113
  • Peer Reviewed
• [Journal Article] Principally tame regular sequences associated with the fourth Painleve hierarchy with a large parameter (2008)
  • Author(s): N.Honda, T. Aoki
  • Journal Title: Proceedings of the Japan academy 84,A Pages: 42-47
  • NAID: 40015931130
  • Peer Reviewed
• [Journal Article] The no-response approach and its relation to non-interactive methods for the inverse problem (2008)
  • Author(s): N.Honda, R.Potthast,G. Nakamura, M. Sini
  • Journal Title: Ann. Math. Pura Appl. 187 Pages: 187-215
  • Peer Reviewed
• [Presentation] 仮想変わり点の幾何とストークス係数 (2010)
  • Author(s): Naofumi Honda
  • Organizer: 日本数学会
  • Place of Presentation: 名古屋大学 招待講演
  • Year and Date: 2010-09-22
• [Presentation] 仮想変わり点の幾何とストークス係数 (2010)
  • Author(s): 本多尚文
  • Organizer: 平成22年度日本数学会秋季大会、函数方程式分科会特別講演
  • Place of Presentation: 名古屋大学(招待講演)
  • Year and Date: 2010-09-19
• [Presentation] Virtual turning points and Stokes coefficents (2010)
  • Author(s): 本多尚文
  • Organizer: Recent Developments in Resurgent Theory and Related topics, RIMS Symposium
  • Place of Presentation: Kyoto
  • Year and Date: 2010-06-29
• [Presentation] On the number of the turning points of the second kind of the Noumi-Yamada systems with a large parameter (2009)
  • Author(s): T.Aoki, N.Honda, Y.Umeta
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
• [Presentation] A virtual turning point and its geometrical structure II (2008)
  • Author(s): 本多尚文
  • Organizer: Foundation of exact WKB analysis and resurgentce theory, RIMS Symposium
  • Place of Presentation: Kyoto
  • Year and Date: 2008-12-16
• [Presentation] A virtual turning point and its geometrical structure I (2008)
  • Author(s): 本多尚文
  • Organizer: Foundation of exact WKB analysis and resurgentce theory, RIMS Symposium
  • Place of Presentation: Kyoto
  • Year and Date: 2008-12-15
• [Presentation] On the deformation of the Riemann manifold underlying a virtual turning point (2008)
  • Author(s): 本多尚文
  • Organizer: New approach to analytic equations-transformation theory, singular solutions and Stokes problem, RIMS Symposium
  • Place of Presentation: Kyoto
  • Year and Date: 2008-09-25