Analysis of substitution and its application

替代分析及其应用

• 批准号: 15540114
• 负责人: ITO Shunji
• 金额: $ 1.66万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540114/
• 关键词: substitution; fractal; quasi crystal; quasi-periodic tiling; Pisot number; Markov partition; タイリング; フピゾ数; 連分数; β-展開

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.)

1）在代换满足（1）么模Pisot不可约条件的假设下，成功地证明了：存在原子曲面族，原子曲面上的动力系统同构于环面上的旋转，称为区域交换变换; 2）在代换不满足不可约条件的情况下，我们得到了区域交换变换与旋转不同构，但与旋转的诱导变换同构的结果。3）我们将深入研究不满足Pisot条件的替换，并成功地得到了结果（见11.参考文献，“Tilings Associated with non-Pisot Matrices”（Annal. Instiiut Fourier，Grenoble（2006）with M. Furukado和E.阿胡尔罗宾逊，Jr.）

项目成果

Purely periodic β-expansions with Pisot base

Pisot 基的纯周期性 β 展开式

• 期刊: Proceeding AMS (発表予定)(To appear)
• 作者: S.ITO;H.RAO
• 通讯作者: H.RAO

Purely periodic β -expansions with Pisot unit base

以 Pisot 单位为基础的纯周期性 β 展开

• 发表时间: 2005
• 期刊: Proc. Amer. Math. Soc. 133・4
• 作者: S.ITO;H.RAO
• 通讯作者: H.RAO

Generating Method of Boundaries of Digit Tiles

数字瓦片边界的生成方法

• 发表时间: 2005
• 期刊: Commentarii Mathematici Universitatis Sancti Paulis 54・2
• 作者: M.FURUKADO;S.ITO;M.OGAWA
• 通讯作者: M.OGAWA

On simultaneous approximation to (a, a2) with α3+ kα-1= 0

同时逼近 (a, a2) 且 α3+ kα-1= 0

• 发表时间: 2003
• 期刊: J. Number Theory 99・2
• 作者: J.FUJII;H.HIGASHINO;S.ITO;S.YASUTOMI
• 通讯作者: S.YASUTOMI

Atomic surfaces, tilings and coincidence I. Irreducible case

• DOI: 10.1007/bf02771781
• 发表时间: 2006-01-01
• 期刊: ISRAEL JOURNAL OF MATHEMATICS
• 影响因子: 1
• 作者: Ito, Shunji;Rao, H.
• 通讯作者: Rao, H.