| Project/Area Number |
26400080
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
KATO Hisao 筑波大学, 数理物質系, 教授 (70152733)
HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
MIURA Takeshi 新潟大学, 自然科学系, 教授 (90333989)
TAKAGI Hiroyuki 信州大学, 理学部, 教授 (20206725)
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 関数空間 / 荷重合成作用素 / 線形作用素 / リーマン多様体 / 射影極限の力学系 / 等長変換 / 一般射影極限 / 無限次元 / カオス |
|---|
| Outline of Final Research Achievements |
We studied isometries of continuous function spaces. A detailed analysis was made on the extreme points of the dual spaces, which yielded some novel Banach-Stone type theorems on isometries (i) of continuous function spaces over compacta with characteristic topology and (ii) of continuous section spaces of Banach space bundles. The results were applied to the study of isometries on continuously differential function spaces over compact Riemannian manifolds. Some families of norms on the function spaces are defined and a Banach-Stone type theorem for these norms was proved. The results were applied to study continuous perturbations of norms and induced deformations of associated isometry groups. The deformation-aspects of isometry groups are shown to be closely related to the geometry of the underlying manifolds.
We also studied topology and dynamics of generalized inverse limits. We made use of the multivalued bonding-function-setup to produce a minimal dynamics on the Cantor set.
|
