2016 Fiscal Year Final Research Report
Research on integrable dynamical systems using geometric methods
| Project/Area Number |
25400106
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | パンルヴェ方程式 / 力学系 / 有理曲面 / モノドロミー |
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| Outline of Final Research Achievements |
We have found a general explicit formula for obtaining the differential Painleve equation from monodromy preservation deformation of the Fuchs type linear ordinary differential equations. We also formulated it as a discrete Hamiltonian system.
Regarding deautonomization of isomorphic mappings of a rational elliptic surfaces, we have formulated a method to derive the corresponding discrete Painleve equation to a choice of an elliptical fiber. The key to this is a method of constructing a map from the action on the Picard group, and we found a general formula for that. In addition, we have discovered symmetries which were not known so far for the simplified version of the resulting elliptic difference Painleve equations.
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| Free Research Field |
可積分系
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