Tropical geometry and integrable systems
| Project/Area Number |
19740086
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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 | Osaka University |
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Principal Investigator |
NOBE Atsushi Osaka University, 教育学部, 准教授 (80397728)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,470,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | 解析学 / 関数方程式論 / 数理物理学 / トロピカル幾何 / 可積分系 / トロピカル楕円曲線 / 超離散QRT写像 / 可解カオス系 / テータ関数 / 加法公式 / Hesseの3次曲線 / モヂュラー変換 / トロピカル幾何学 / 超離散系 / 楕円曲線 / QRT写像 |
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| Research Abstract |
We construct an 8-parameter family of two-dimensional bi-piecewise linear maps in terms of the addition of the points on tropical elliptic curves, and obtain the general solution for each member of the family. Through the ultradiscretization procedure, we associate the family with an 18-parameter family of two-dimensional birational maps called the QRT map including its general solutions. Similarly, applying such technique to solvable chaotic maps induced from the duplication of points on tropical elliptic curves, we obtain their general solution and clarify the correspondence to the rational maps induced from the duplication of points on elliptic curves. Moreover, we show that there exists a family of cellular automata each of which has a property called the linearizability. Then we obtain a formula concerning the fundamental period with respect to the time evolution of the family imposing periodic boundary conditions.
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Report
(4 results)
Research Products
(41 results)
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[Presentation] カオス系の超離散化2009
Author(s)
梶原健司, 金子昌信, 野邊厚, 津田照久
Organizer
研究集会「非線形波動研究の現状と将来」
Place of Presentation
九州大学応用力学研究所
Year and Date
2009-11-20
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