Project/Area Number  09640226 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Japan Women's University 
Principal Investigator 
TOMIYAMA Jun Japan Women's Univ., Fac.of Sci., Professor, 理学部, 教授 (30006928)

CoInvestigator(Kenkyūbuntansha) 
FUJISAKI Rieko Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (30060635)
MINEMURA Katsuhiro Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (20060684)
OEDA Kazuo Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (10060675)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1998 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1997 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  C^*algebra / Topological dynamical system / Elementary sets of dynamical system / Orbit equivalence / Heat convection equation / Foliation / C^*環 / 位相力学系 / 力学系の初等集合 / 軌道同値 / 熱対流方程式 / 葉層構造 / C^*環 / C^* 環 / 充足群 
Research Abstract 
The followings are main points of our results during the academic years through 1997 to 1998(Heisei 910). 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 Calgebras 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 CZcrossed product with its analysis andthe other is to distinguish the ideal of homeomorphism Calgebras 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 Calgebraic 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.
