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。图形自图的传递性与强传递性之间的关系，2。图形自图的驳船 - 马丁类型定理，其周期点非常致密，（T.Hosaka）3。作用在双曲线或CAT（0）空间的组的极限集的内部，4。 Coxeter组边界的密集子集，5。具有二维戴维斯 - 温伯格复合体的Coxeter系统，6。二面gropus的Coxeter系统的强刚度和强烈反射刚度，7。 Coxeter组的抛物线亚组的边界，8。 Coxeter系统边界的最小性，9。地球空间的反射群，（M.Kimura）10。复杂Quadric中订单2的Frenet曲线的一致类别，11。将空间作为工会或局部紧凑子空间的分区和（y.hattori）12的可能性。在可衡量的空间中，没有小的跨金融紧凑度的上限。

项目成果

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

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

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

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 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