Spectral problem on quasi-periodic structure
| Project/Area Number |
21540010
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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 |
Algebra
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| Research Institution | Niigata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Kazushi 高知大学, 自然科学系, 准教授 (00253336)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 準周期構造 / タイル張り / 記号力学系 / スペクトル / 数系 / 置換規則 / Pisot数 / 自己相似 / フラクタル |
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| Research Abstract |
With Jeong-Yup Lee we developed a practical algorithm to check pure discreteness of translation dynamics of the orbit closure of self-affine tilings with Pisot family condition. Pisot numbers often appears as dilation constants of self-inducing structures. We observed similar Pisot dilations in the self-similar dissection problem of planar shapes in the joint paper with R. Okazaki, J. Luo, J. Thuswaldner and W. Steiner. With Benoit Loridant, we succeeded in giving a standard parameterization of boundaries of self-affine tilings and showed its effectiveness in their topological classification.
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Report
(4 results)
Research Products
(70 results)
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[Presentation] Pentagonal domain exchange2009
Author(s)
Shigeki Akiyama
Organizer
Workshop on Measurable and Topological Dynamical Systems in Asia
Place of Presentation
Ajou University, Suwon, Korea
Year and Date
2009-06-20
Related Report
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