Limiting procedure and behavior of solutions for integrable dynamical systems
| Project/Area Number |
19740084
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
TAKENAWA Tomoyuki Tokyo University of Marine Science and Technology, 海洋工学部, 准教授 (70361805)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,020,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 可積分系 / パンルヴェ方程式 / トロピカル幾何学 / 離散系 / 力学系 / ハミルトン系 / モノドロミー / 楕円曲面 / 超離散化 / トロピカル幾何 / テータ関数 / 実代数幾何 / セルオートマトン / 双有理写像 |
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| Research Abstract |
I studied how property of solutions reflects through limiting procedure from discrete dynamical systems to continuous or ultra-discrete systems. Especially, on ultra-discrete systems, by using tropical algebraic geometry, I found tropical spectral curve for ultra-discrete periodic Toda lattice, which is essentially equivalent to the integrable box and ball system. On discrete systems, I clarified relationship between some dynamical systems and higher dimensional rational variety. Moreover, using rational elliptic surfaces, I classified integrable autonomous systems.
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Report
(6 results)
Research Products
(47 results)
