Painleve equations and infinite integrable systems

• Project/Area Number: 19840039
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: 津田 照久 Kyushu University, 大学院・数理学研究院, 助教 (00452730)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,702,000 (Direct Cost: ¥2,360,000、Indirect Cost: ¥342,000); Fiscal Year 2008: ¥1,482,000 (Direct Cost: ¥1,140,000、Indirect Cost: ¥342,000); Fiscal Year 2007: ¥1,220,000 (Direct Cost: ¥1,220,000)
• Keywords: パンルヴェ方程式 / 可積分系

Research Abstract

ワイル群の, 良い幾何学的な背景を持つような新しい実現を構成した。これは高次元の有理代数多様体に擬正則写像として作用し, また可積分系において重要なタウ函数は高さ関数の類似として幾何的に定まる。ルート系がアフィン型の場合には, 付随する力学系は既知の高階q-パンルヴェ方程式を全て含むような一般的な枠組みを提供し, 今後の研究に広い応用を持つものと期待される。またUC階層と呼ばれる無限次元可積分系とモノドロミー保存変形(パンルヴェ方程式・ガルニエ系)との関係を, 波動関数の満たす線形問題を経由することで, 明らかにした。

Research Products

• [Journal Article] Universal character and q-Painleve equations (2009)
  • Author(s): T.Tsuda
  • Journal Title: Math.Ann (in press)
• [Journal Article] Tropical representation of Weyl groups associated with certain rational varieties (2009)
  • Author(s): T.Tsuda and T.Takenawa
  • Journal Title: Adv.Math (in press)
• [Journal Article] Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve (2009)
  • Author(s): K.Kajiwara, M.Kaneko, A. Nobe and T.Tsuda
  • Journal Title: Kyushu J. Math (in press)
  • NAID: 130000135287
• [Journal Article] A geometric approach to tau-functions of difference Painleve equations (2008)
  • Author(s): T.Tsuda
  • Journal Title: Lett.Math.Phys 85 Pages: 65-78
• [Journal Article] Ultradiscretization of solvable one-dimensional chaotic maps (2008)
  • Author(s): K.Kajiwara, A.Nobe and T.Tsuda
  • Journal Title: J.Phys.A : Math.Theor 41
• [Journal Article] A geomotric appreach to fou-funcfions of differencc Painleve equations (2008)
  • Author(s): Teruhisa Tsuda
  • Journal Title: Letters in Mathematical Physics 85 Pages: 65-78
  • Peer Reviewed
• [Journal Article] UHraoliscrefiyation of solvable one-dimensional chactic maps (2008)
  • Author(s): K. Kajinara, A. Nebe, T. Tsuda
  • Journal Title: J. Phys. A : Math. Theor 41 Pages: 395202-395202
  • Peer Reviewed
• [Journal Article] A class of integrable and nonintegrable mappings and their dynamics (2007)
  • Author(s): T.Tsuda, B.Grammaticos, A.Ramani and T.Takenawa
  • Journal Title: Lett.Math.Phys 82 Pages: 39-49
• [Journal Article] A class of integrable and nonintegrable mappings and their dynamics (2007)
  • Author(s): Teruhisa Tsuda, et. al.
  • Journal Title: Letters in Mathematical Physics 82 Pages: 39-49
  • Peer Reviewed
• [Presentation] KP・UC階層とパンルベ・ガルニエ系 (2009)
  • Author(s): 津田照久
  • Organizer: 超幾何方程式研究会
  • Place of Presentation: 神戸大学
  • Year and Date: 2009-01-06
• [Presentation] A geometric approach to tropical Weyl group actions and q-Painleve equations (2008)
  • Author(s): T.Tsuda
  • Organizer: Workshop "Geometry and Arithmetic arround Hypergeometric Functions"
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach (Germany)
  • Year and Date: 2008-10-01
• [Presentation] 普遍指標と可積分系, パンルヴェ方程式 (2008)
  • Author(s): 津田照久
  • Organizer: 研究集会「可積分系数理の拡がり」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-08-12
• [Presentation] 普遍指標と可積文系、パンルヴェ方程式 (2008)
  • Author(s): 津田 照久
  • Organizer: RIMS研究集会“可積文系の拡がり"
  • Place of Presentation: 京都大学
  • Year and Date: 2008-08-12
• [Presentation] A geometric approach to tropical Weyl group actions and q-Painleve equations (2008)
  • Author(s): T.Tsuda
  • Organizer: International Conference "From Painleve to Okamoto"
  • Place of Presentation: The University of Tokyo (Japan)
  • Year and Date: 2008-06-10
• [Presentation] A geometric approach to tropical Weyl group actions and q-Painleve equations (2008)
  • Author(s): T.Tsuda
  • Organizer: The Banach Center Conference "Second Workshop on Nonlinearity and Geometry. Darboux Days"
  • Place of Presentation: Poznan (Poland)
  • Year and Date: 2008-04-18
• [Presentation] A geometric approach to tropical Weyl group actions and q-Painleve equations (2007)
  • Author(s): T.Tsuda
  • Organizer: Workdhop on"Isolevel sets of the integrable systems 2007"
  • Place of Presentation: 慶応大学
  • Year and Date: 2007-06-20
• [Presentation] A geometric approach to tropicae weyl group actions and q-Painleve eguations (2007)
  • Author(s): 津田 照久
  • Organizer: Workshop on the TSO level Sets of the Integrable systems2007
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2007-06-20