Construction of the integrability criteria for discrete dynamical systems in view of their algebraic structures
| Project/Area Number |
15H06128
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kansai University (2016)
The University of Tokyo (2015) |
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Principal Investigator |
Kanki Masataka 関西大学, システム理工学部, 助教 (20755897)
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 可積分系 / 力学系 / 差分方程式 / 互いに素条件 / 離散力学系 / 解析学 / 数理物理 / 離散可積分系 / 代数的エントロピー / 特異点閉じ込め |
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| Outline of Final Research Achievements |
We have costructed one of the integrability criteria for discrete dynamical systems, by investigating the algebraic structures of the equations in detail.
We call this criterion the coprimeness condition, and have applied the criterion to many of the known integrable discrete dynamical systems.
We have constructed new types of 'quasi-integrable' equations, by our method of coprimeness-preserving extensions of the already known integrable and non-integrable equations. By introducing several parameters in the terms of the discrete KdV equation and the discrete Toda equation, we have obtained coprimeness-preserving and non-integrable (in the sense that the degrees of their iterates grow exponentially) extension of these discrete equations.
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Report
(3 results)
Research Products
(9 results)
