Research of a boundary of a Coxeter system and dimension theory

Coxeter系统的边界和维数论研究

• 批准号: 16540067
• 负责人: YOKOI Katsuya
• 金额: $ 2.3万
• 依托单位: Shimane University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540067/
• 关键词: transitive; graph; Coxeter group; compactness degree; コンパクト指数; コクセター; コクセター系; 区分的単調写像; 次元関数

We studied :(K.Yokoi)1. the relation between transitivity and strong transitivity for graph self-maps,2. a Barge-Martin type theorem for graph self-maps for which the set of periodic points is dense,(T.Hosaka)3. the interior of the limit set of a group acting on a hyperbolic or CAT(0) space,4. dense subsets of the boundary of a Coxeter groups,5. Coxeter systems with two-dimensional Davis-Vinberg complexes,6. strong rigidity and strong reflection rigidity of Coxeter systems of dihedral gropus,7. boundaries of parabolic subgroups of Coxeter groups,8. the minimality of the boundary of a Coxeter systems,9. reflection groups of geodesic spaces,(M.Kimura)10. congruent classes of Frenet curves of order 2 in the complex quadric,11. the possibility of different presentations of spaces as unions or partitions of locally compact subspaces, and(Y.Hattori)12. there is no upper bound of small transfinte compactness degree in metrizable spaces.

我们研究了：（K.Yokoi）1。图自映射的传递性和强传递性之间的关系；2．周期性点集密集的图自映射的 Barge-Martin 型定理，(T.Hosaka)3。作用于双曲或 CAT(0) 空间的群的极限集的内部，4。 Coxeter群边界的稠密子集，5。具有二维 Davis-Vinberg 复合体的 Coxeter 系统，6。二面体Coxeter系统的强刚度和强反射刚度，7． Coxeter群的抛物线子群的边界，8。 Coxeter 系统边界的极小性，9。测地空间的反射群，（M.Kimura）10。复二次曲面中 2 阶 Frenet 曲线的全等类，11。空间作为局部紧凑子空间的并集或划分的不同表示的可能性，以及（Y.Hattori）12。可度量空间中不存在小超限紧度的上限。

项目成果

Dense subsets of the boundary of a Coxeter system

Coxeter 系统边界的密集子集

• 发表时间: 2004
• 期刊: Proceedings of the American Mathematical Society 132
• 作者: T.Furumochi;S.Murakami;Y.Nagabuchi;T.Hosaka
• 通讯作者: T.Hosaka

Stabilities in Volterra difference equations or a Banach space

Volterra 差分方程或 Banach 空间中的稳定性

• 发表时间: 2004
• 期刊: Fields Institute Communications 42
• 作者: T.Furumochi;S.Murakami;Y.Nagabuchi
• 通讯作者: Y.Nagabuchi

The behaviour of dimension functions on unions of closed subsets

闭子集并集上维度函数的行为

• 发表时间: 2004
• 期刊: J.Math.Soc.Japan 56
• 作者: M.Charalambous;V.Chatyrko;Y.Hattori
• 通讯作者: Y.Hattori

Strong transitivity and graph maps, Bulletin of the Polish Academy of Sciences

强及物性和图表，波兰科学院通报

• 发表时间: 2005
• 期刊: Mathematics 53
• 作者: T.A.Burton;T.Furumochi;T.Furumochi;K.Yokoi
• 通讯作者: K.Yokoi

Stabilities in FDEs by Schauder's theorem

• DOI: 10.1016/j.na.2005.02.057
• 发表时间: 2005-11
• 期刊: Nonlinear Analysis-theory Methods & Applications
• 影响因子: 1.4
• 作者: T. Furumochi