Study of Foliations and Dynamical Systems
| Project/Area Number |
25400099
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Nihon University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Keywords | 葉層構造 / 調和測度 / 葉の位相 / 円周上の同相写像 / Liouville 数 / 極小流れ / 円周上の群作用 / 群の不変生成性 / 群の左不変順序 / 群の左順序 / 左順序の力学的実現 / 力学系 / 微分同相写像群 / 葉向調和関数 / 微分可能同相群 / Anosov 流れ / 接触流れ / 軌道同値 |
|---|
| Outline of Final Research Achievements |
We studied orientation preserving infinitely differentiable diffeomorphisms of the circle whose rotation numbers are the given Liouville numbers. We showed that the diffeomorphisms whose invariant measures have the Hausdorff dimension 0 form a residual subset. We also studied the types of the orbit equivalence classes that the diffeomorphims determine together with the Lebesgue measure. We showed that the diffeomorphisms which take the given type form a dense subset. We also considered foliations on compact manifolds whose leaves are hyperbolic Riemann surfaces. We obtained sufficient conditions for the associated leafwise horocycle flows to be minimal.
|
Report
(6 results)
Research Products
(20 results)
