2015 Fiscal Year Final Research Report
Pisot conjecture on substitutive dynamical systems
| Project/Area Number |
24540012
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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 |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Kazushi 高知大学, 理学部, 准教授 (00253336)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | ピゾ数 / 置換規則 / 自己誘導構造 / タイリング / 自然拡大 / 概周期構造 / 準結晶 |
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| Outline of Final Research Achievements |
Substitutive dynamical system models self-inducing structure appears in general dynamical systems. It is generated by a substitution rule on finite letters. Such system realized as self-similar tiling can not be strongly mixing and whether it is weakly mixing or not is described by whether the dilation is a Pisot number.
We studied the well-known conjecture in this area which asserts that every irreducible Pisot substituion is pure discrete. As a result with J.Y.Lee we elucidated relationship between several coincidence conditions. Further with J.Y.Lee and F.Gahler, we did a systematic valification of the conjecture up to trace 2. All of them are pure discrete, we did not find a counter example.
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| Free Research Field |
数論
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