Analysis for pre-fractal structures in guasiperiodic filings
| Project/Area Number |
18540126
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kochi University |
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Principal Investigator |
KOMATSU Kazushi Kochi University, Faculty of Science, Associate Professor (00253336)
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| Co-Investigator(Kenkyū-buntansha) |
NOMAKUCHI Kentaro Kochi Univ., Faculty of Science, Professor (60124806)
NAKANO Fumihiko Kochi Univ., Faculty of Science, Associate Professor (10291246)
AKIYAMA Shigeki Niigata Univ., Faculty of Science, Associate Professor (60212445)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | tiling / quasi-neriodicity / matching rule / substitution rule / non-periodicity / dynamical system / self-similarity / projection method / 準周期性 / フラクタル / 回転列 / 準結晶 / 貼り合わせルール / 非周期性 / モジュライ空間 |
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| Research Abstract |
The summary of research results is as follows
1. We construct a sequentially compact spam of patches in 2 and higher dimensional oases By using this constnction, we analyze certain symmetries of tilings obtained by substitution rules we give explicitly the construction of tilings with rotational symmetries in some examples(a Penrose tiling, an Ammann-Beenker tiling a Danzer tiling).
2. We give a mathematical model of n-membered ringed hydrocarbon molecules, and study the topology of a configuration space of the model. Assuming requited conditions for ringed molecules, we prove that its configuration space is diffeomorphic to (n-4)-dimensional sphere for n> 4. This result gives an appropriate explanation of the configuration space of n-membered ringed hydrocarbon molecules when n= 5, 6.
3. We consider the point process composed of the eigenvalues and corresponding localization centers, and showed that in the infinite volume limit it converges to the Poisson point process.
4. We studied the coding of 1-dimensional irrational rotation with arbitray decomposition of the unit interval. The coded sequence has recursively renewable structure, and we then classify when this procedure is described by stationaly process. It tured out that this happens when and only when all decomposition points, the initial value and the speed of rotations are in the same real quadratic field.
5. We studied the points on the boundary of SRS region whether they always produces eventually periodic orbits or not. Remarkably we prove that this periodicity is valid in the case of golden mean. This study extends to recent further researches on discretized rotation having self-indudng structures.
6. We obtain a theorem on stable unextendibility of R-vector bundles over (2n+1)-dimensional standard lens space mod 3 improving some known results.
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Report
(3 results)
Research Products
(23 results)
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[Presentation] 双曲平面タイリングの非周期性について2007
Author(s)
岸本 晋哉, 小松 和志
Organizer
準周期構造のスペクトル解析と関連する話題
Place of Presentation
京都大学数理解析研究所
Year and Date
2007-11-19
Description
「研究成果報告書概要(和文)」より
Related Report
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