Study of transfer operator for geodesic flow and the semiclassical zeta function
| Project/Area Number |
22340035
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Kyushu University |
|---|
Principal Investigator |
TSUJII Masato 九州大学, 数理(科)学研究科(研究院), 教授 (20251598)
|
|---|
| Project Period (FY) |
2010-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2014: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2010: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
|
|---|
| Keywords | 力学系 / 測地流 / カオス / 転送作用素 / スペクトル / エルゴード理論 / 力学系理論 / 力学系のゼータ関数 / 量子カオス / 周期軌道 / フランス / 準古典解析 / アノソフ流 / アノソフ微分同相 / 半古典解析 / 関数解析 / ゼータ関数 |
|---|
| Outline of Final Research Achievements |
In this research project, we studied dynamical systems exhibiting typically chaotic behavior (especially, the geodesic flow which describes the motion of free particle on negatively curved space) and develop a theory to understand their fine statistical properties by analyzing spectral properties of associated transfer operators. The main result obtained in this research project proves that, for geodesic flows on negatively curved manifolds (or more generally for contact Anosov flows) the generator of transfer operators has discrete spectrum and has a band structure, that is, the discrete eigenvalues are contained in several bands parallel to the complex plane. Further we obtained the corresponding results on dynamical zeta functions. This is a significant progress in the related fields.
|
Report
(6 results)
Research Products
(14 results)
