Study of functional analytic methods in dynamical system theory
| Project/Area Number |
18340044
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyushu University (2007-2009)
Hokkaido University (2006) |
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Principal Investigator |
TSUJII Masato Kyushu University, 大学院・数理学研究院, 教授 (20251598)
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| Co-Investigator(Kenkyū-buntansha) |
新居 俊作 九州大学, 数理学研究院, 准教授 (50282421)
石井 豊 九州大学, 数理学研究院, 准教授 (20304727)
由利 美智子 北海道大学, 大学院・理学研究院, 教授 (70174836)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHII Yutaka 九州大学, 大学院・数理学研究院, 准教授 (20304727)
NII Shunsaku 九州大学, 大学院・数理学研究院, 准教授 (50282421)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥14,970,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥2,670,000)
Fiscal Year 2009: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2008: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2006: ¥3,400,000 (Direct Cost: ¥3,400,000)
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| Keywords | 力学系 / 関数解析 / エルゴード理論 / カオス / ゼータ関数 / 転移作用素 / スペクトル / 量子カオス / 双曲力学系 |
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| Research Abstract |
We studied functional analytic methods in dynamical systems theory and ergodic theory. For hyperbolic and partially hyperbolic dynamical systems, we constructed function spaces on the phase space adapted to the system so that the corresponding transfer operators have good spectral properties on them. As an application, we get precise results on Ruelle-Pollicott resonance and analytic properties of dynamical zeta functions especially for expanding semi-flows and geodesic flows on negatively curved manifolds.
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Report
(6 results)
Research Products
(50 results)
