| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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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