Analytic study of Painleve equations and a nelated clans of equation
Grant-in-Aid for Scientific Research (B)
|Allocation Type||Single-year Grants |
|Research Institution||Keio University |
SHIMOMURA Shun Keio University, Facualry of Science and Technlogy, Prof. (00154328)
TANI Atusi Keio University, Faculty of Science and Technology, Prof (90118969)
SHIOKAWA Iekata Keio University, Faculty of Science and Technology, Honorary Prof (00015835)
KIMURA Hironobu Kumamoto University, Faculty of Science and Technology, Professor (40161575)
HANAOKA Yoshishige Kumamoto University, Faculty of Science and Technology, Professor (30208665)
ISHIGAKI Katsuya Nippon Insitute of Technology, Faculty of Engineering, Associate Professor (60202991)
菊池 紀夫 慶應義塾大学, 理工学部, 教授 (80090041)
藤解 和也 金沢大学, 大学院・自然科学研究科, 助教授 (30260558)
|Project Period (FY)
2005 – 2007
Completed(Fiscal Year 2007)
|Budget Amount *help
¥5,050,000 (Direct Cost : ¥4,600,000、Indirect Cost : ¥450,000)
Fiscal Year 2007 : ¥1,950,000 (Direct Cost : ¥1,500,000、Indirect Cost : ¥450,000)
Fiscal Year 2006 : ¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 2005 : ¥1,600,000 (Direct Cost : ¥1,600,000)
|Keywords||Painleve equations / Ganier system / quasi-Painleve property / Fibonacci numbers / Painleve方程式 / Garnier系 / 準Painleve性 / 特異点 / Painleve equation / 準パンルヴェ性|
1. We found a class of nonlinear ordinary differential equations containing the first Painleve equation such that each equation admits the quasi-Painleve property, and discussed the global multi-valuedness of their solutions. We also found a similar clean of equations containing the second Painleve equation.
2. For solutions of the fifth Painleve equation, we examined value distribution in a sectonial domain. Under a certain condition, we proved the equi-distribution of values.
3. For a degenerate Garnier system corresponding to the first Painleve equation, we obtain an asymptotic solution around a singular locus.
4. We examined algebraic independence and algebraic relations for reciprocal rums of Fibonacci numbers. We also discussed their relation to zeta values.
Research Products (23results)