2016 Fiscal Year Final Research Report
Studies on global behavior of solutions to linear differential equations and isomonodromic deformations
| Project/Area Number |
25800082
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | モノドロミ保存変形 / 有限鏡映群 / 有理関数近似 |
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| Outline of Final Research Achievements |
In this study, we mainly treated the following two subjects:1)Construction of transformations for linear differential equations by means of rational approximations. 2)Isomonodromic deformations of Okubo systems and flat structures.
1) is based on joint works with Teruhisa Tsuda.We constructed Schlesinger transformations for linear differential equations by means of Hermite-Pade approximation and obtained determinant structures for solutions to isomonodromic deformations. 2) is based on joint works with Mitsuo Kato and Jiro Sekiguchi. We clarified the relation between isomonodromic deformations of Okubo systems and flat structures. As its application, we obtained flat structures on the orbit spaces of complex reflection groups and descriptions of solutions to the Painleve equation in terms of potential vector fields.
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| Free Research Field |
数学
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