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）假设替代是（1）单二型，皮索，不可约束的条件，我们成功地证明，存在称为原子表面的一组套装和在原子表面上的动力学系统，被称为域交换所称为torus of torus of contibal of contibal of contibil.2）在范围内，我们在范围内均不满意。交换转化不是旋转的同构，而是与旋转转化的诱导转化是同构的。3）我们将深入研究不满足双皮特条件的替换，我们成功地获得了结果（请参阅11。参考文献，“与非PISOT Matrices相关的Tilings”（Annal。Instric。Instiiiut。Instiiiut.Instiiiut and ful for funier and ruk and arh and anhh and and anh anh nhh and anh n. 2006年）。小罗宾逊）

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

Tilings from some non-irreducible, Pisot substitutions

一些不可约的皮索替换的平铺

• 发表时间: 2005
• 期刊: Discrete Math. Theor. Comput. Sci. 7・1
• 作者: H.EI;S.ITO
• 通讯作者: S.ITO