Painleve systems, hypergeometric systems and dynamical systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400102
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: Iwasaki Katsunori 北海道大学, 理学(系)研究科(研究院), 教授 (00176538)
• Co-Investigator(Renkei-kenkyūsha): UEHARA Takato 佐賀大学, 理工学部, 准教授 (40613261)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: パンルヴェ方程式 / 超幾何関数 / 力学系 / ハミルトン構造 / 周期解 / ガンマ乗積表示 / 隣接関係式 / 対称性

Outline of Final Research Achievements

Hypergeometric equations are linear differential equations solved by an important class of functions called hypergeometric functions, while in certain sense Painleve equations may be thought of as nonlinear analogues of hypergeometric equations. Because of their nonlinearity, the study of Painleve equations requires various methods from dynamical systems. We constructed the phase space of a Painleve equation and gave a geometric characterization of it as an orbifold Hamiltonian dynamical system. We also discussed periodic solutions to another Painleve equation. As for hypergeometric functions we focused our attention on spacial-value formulas, especially on gamma product formulas, and obtained necessary conditions of arithmetic flavor for the existence of such formulas.

Free Research Field

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