2004 Fiscal Year Final Research Report Summary
Global study of functional equations and special functions
| Project/Area Number |
15540212
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Keio University |
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Principal Investigator |
SHIMOMURA Shun Keio Univ., Fac.of Sci.and Tech., Professor, 理工学部, 教授 (00154328)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUCHI Norio Keio Univ., Fac.of Sci.and Tech., Professor, 理工学部, 教授 (80090041)
TANI Atsushi Keio Univ., Fac.of Sci.and Tech., Professor, 理工学部, 教授 (90118969)
SHIOKAWA Iekata Keio Univ., Fac.of Sci.and Tech., Professor, 理工学部, 教授 (00015835)
NAKANO Minoru Keio Univ., Fac.of Sci.and Tech., Assistant Professor, 理工学部, 講師 (00051607)
TOHGE Kazuya Kanazawa Univ., Fac.of Tech., Associate Professor, 大学院・自然科学研究科, 助教授 (30260558)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Painleve equations / growth order / value distribution / Painleve hierarchy / Riccati equation |
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| Research Abstract |
1.For Painleve transcendents of I, II, IV types, we estimated the growth order. The results are as follows : P_I=5/2 for I ; 3/2【less than or equal】P_<II>【less than or equal】3 for II ; and 2【less than or equal】P_<IV>【less than or equal】4 for IV.
2.We proved the Painleve property for all Painleve equations.
3.We considered solutions of the third and the fifth Painleve equations on the universal covering space, and obtained some estimates for the growth order.
4.We obtained a lower estimate for the growth order of solutions of the first Painleve hierarchy, and also estimated the frequency of poles and α-points of them.
5.We presented a series of systems of differential equations which is equivalent to the first Painleve hierarchy, and proved the Painleve property.
6.We estimated the growth order of solutions of Riccati equations with doubly periodic coefficients.
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