Complexity structure analysis on the orbits of solutions of nonlinear partial differential equations by p-adic analysis
| Project/Area Number |
24540180
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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 | Kumamoto University |
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Principal Investigator |
NAITO Koichiro 熊本大学, 自然科学研究科, 教授 (10164104)
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| Co-Investigator(Kenkyū-buntansha) |
SHIROMOTO Keisuke 熊本大学, 大学院自然科学研究科, 教授 (00343666)
MISAWA Masashi 熊本大学, 大学院自然科学研究科, 教授 (40242672)
WADA Takeshi 島根大学, 大学院総合理工学研究科, 教授 (70294139)
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| Co-Investigator(Renkei-kenkyūsha) |
OGAWA Takayoshi 東北大学, 大学院理学研究科, 教授 (20224107)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | P-進数論 / 格子理論 / 暗号理論 / 力学系 / 非線形偏微分方程式 / 連分数展開 / p-進数論 / 関数解析 |
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| Outline of Final Research Achievements |
Analyzing simultaneous rational approximations of irrational p-adic numbers by using multi-dimensional p-adic approximation lattices, we investigate some recurrent properties of discrete orbits given by quasi-periodic dynamical systems, the frequencies of which are weak Liouville p-adic numbers and we show some unpredictability properties of the orbits. For the symbolic dynamical systems given by the coefficient sequences of expansions of p-adic numbers we give some inequality relations between the recurrent dimensions and the topological entropy of these systems.
For the shortest vector problems of p-adic approximation lattices we compare the theoretical solutions given by the simultaneous approximation problems (SAP) and the numerical solutions estimated by the LLL algorithm. By using these results we propose a new lattice based cryptosystem, the private keys of which are the SAP solutions of p-adic lattices.
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Report
(4 results)
Research Products
(64 results)
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[Presentation] From codes to matroid and back2014
Author(s)
Keisuke Shiromoto
Organizer
The 3rd Taiwan-Japan Conference on Combinatorics and its Applications (3TJCCA)
Place of Presentation
National Chiayi University, Chiayi City, Taiwa
Related Report
Invited
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[Presentation] Codes over rings and matroids2012
Author(s)
Keisuke Shiromoto
Organizer
The 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
Place of Presentation
University of New South Wales (Sydney, Australia)
Related Report
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