On the interplay between C^*-algebras and topological dynamical systems

关于 C^*-代数和拓扑动力系统之间的相互作用

• 批准号: 09640226
• 负责人: TOMIYAMA Jun
• 金额: $ 1.66万
• 依托单位: Japan Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640226/
• 关键词: C^*-algebra; Topological dynamical system; Elementary sets of dynamical system; Orbit equivalence; Heat convection equation; Foliation; C^*-環; C^* 環; 充足群

The followings are main points of our results during the academic years through 1997 to 1998(Heisei 9-10). Among them, the first four items are carried out by Tomiyama.1.Proved the restricted isomorphism theorem for the best possible wide classes of dynamical systems ; namely obtained the condition between dynamical systems when their associated C-algebras are isomorphic keeping the subalgebras of continuous functions for such a class.2.Introduced the representation theory of dynamical systems as a new stand pointof the theory As consequences, we have reinforced the previous results in this field.3.Cultivated various kinds of ways to attack the general isomorphism problem, among which one is the idea of universal C-Z-crossed product with its analysis andthe other is to distinguish the ideal of homeomorphism C-algebras as good and bad (and most bad) ones together with the characterizations of good ideals. Also analysed the properties of isomophisms from this point.4.Obtained the C-algebraic descriptions of the behavior of nonwandering sets ofdynamical systems, the depths of the Birkhoff center. Among those elementary sets of dynamical systems, only this thing had been remained unsolved for several years.5.Qeda has obtained the global solutions for the initial value problem of the heat convection equation in an exterior domain in the 2 or 3 dimensional Eucidean spaces. For a codimension q Hausdorff foliation having Torus as general leaves in the 4 or 5 dimensional compact manifold, Fujisaki has classified the types of singular leaves with the analysis of their local stabilities.

以下是我们在1997至1998学年（平成9-10）的结果的要点。其中前四项工作是由Tomiyama完成的：1.证明了最佳大类动力系统的限制同构定理;即得到了动力系统的C-代数同构时保持该类连续函数的子代数的条件. 2.引入了动力系统的表示理论，作为动力系统表示理论的一个新的观点. 3.研究了一般同构问题的各种方法，其中一种是泛C-Z-交叉积的概念及其分析，另一种是区分同胚C-代数的理想是好的和坏的（和最坏的）理想，以及好理想的特征。并由此分析了同构的性质。4.得到了动力系统非游荡集行为的C-代数描述，Birkhoff中心的深度。在那些动力系统的基本集合中，只有这一个问题多年来一直没有得到解决。5. Qeda已经得到了2维或3维Eucidean空间中外部区域上热对流方程初值问题的整体解。对于4维或5维紧致流形中的以环面为一般叶的余维q Hausdorff叶理，Fujisaki对奇异叶的类型进行了分类，并分析了它们的局部稳定性.

项目成果

藤崎 リエ子: "Stability of singular leaves of compact Hausdorff foliarions with tori as generic leaves" Tokyo Journal of Mathematics. (予定).

Rieko Fujisaki：“以花托为通用叶子的紧凑 Hausdorff 叶状体的奇异叶子的稳定性”《东京数学杂志》（计划中）。

大枝 一男: "Periodic solutions of the heat convection equations in exterior domains" Proc.Japan Academy. 73(4). 49-54 (1997)

Kazuo Oeda：“外部域热对流方程的周期解”Proc.Japan Academy。73(4) (1997)。

大枝 一男: "Initial value problems for the heat convection equations in exterior domains" Tokyo Journal of Mathematics. 21-2. 359-375 (1998)

Kazuo Oeda：“外部域热对流方程的初值问题”，《东京数学杂志》21-2（1998）。

K.Oeda: "Initial value problems for the heat convection equations in exterior domains" Tokyo Journal of Mathematics. 21-22. 359-375 (1998)

K.Oeda：“外部域热对流方程的初值问题”《东京数学杂志》。

J.Tomiyama: "Bounded topological orbit equivalence and C^*-algebras" Journal of Mathematical Society of Japan. 50-2. 317-329 (1998)

J.Tomiyama：“有界拓扑轨道等价和 C^*-代数”日本数学会杂志。