2005 Fiscal Year Final Research Report Summary
Analysis of substitution and its application
| Project/Area Number |
15540114
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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 | Kanazawa University |
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Principal Investigator |
ITO Shunji Kanazawa Universtiy, Graduate School of Natural Science & Technology, Professor, 大学院・自然科学研究科, 教授 (30055321)
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| Co-Investigator(Kenkyū-buntansha) |
OGAWA Shigeyoshi Ritsumeikan University, Department of Mathematical Science, Professor, 理学部, 教授 (80101137)
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| Project Period (FY) |
2003 – 2005
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| Keywords | substitution / fractal / quasi crystal / quasi-periodic tiling / Pisot number / Markov partition |
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| Research Abstract |
1)On the assumption that the substitution satifies (1) unimodular, Pisot, irreducible condition, we succeeded to prove that, there exists the family of sets called atomic surfaces and the dynamical system on the atomic surfaces, which is called domain exchange transformation, is isomorphic to a rotation on torus.
2)In the case that substitution does not satisfy the irreducible condition, we have the result that the domain exchange transformation is not isomorphic to the rotation, but it is isomorphic to the induced transformation of the rotation.
3)We are going to study deeply the substitution which is not satisfied the Pisot condition, and we succeeded to obtain the result (see 11. REFERENCES, "Tilings Associated with non-Pisot Matrices"(Annal. Instiiut Fourier, Grenoble (2006) with M. Furukado and E. Arhour. ROBINSON, Jr.)
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