2011 Fiscal Year Final Research Report
Complexity analysis on orbits of solutions of nonlinear partial differential equations
| Project/Area Number |
21540191
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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, 大学院・自然科学研究科, 教授 (10164104)
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| Co-Investigator(Kenkyū-buntansha) |
MISAWA Masashi 熊本大学, 大学院・自然科学研究科, 教授 (40242672)
KADOTA Noriya 熊本大学, 大学院・自然科学研究科, 講師 (80185884)
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| Co-Investigator(Renkei-kenkyūsha) |
SHIROMOTO Keisuke 熊本大学, 大学院・自然科学研究科, 教授 (00343666)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 関数方程式 / 準周期性 / フラクタル次元 / 再帰性 / ディオファンタス近似 |
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| Research Abstract |
We show nondeterministic recurrent properties of discrete quasi-periodic orbits by estimating the GAP values between upper and lower recurrent dimensions. We also show the relations between the GAP values and the topological entropy, which indicates its chaotic complexity, and then we clarify its unpredictability.
We show the unpredictability of the quasi-periodic orbits with multi-frequencies, which are an extremal irrational number and its square, by estimating the positive gaps of their recurrent dimensions.
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