2017 Fiscal Year Final Research Report
Study of Foliations and Dynamical Systems
| Project/Area Number |
25400099
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| 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 |
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| 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.
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| Free Research Field |
葉層構造と力学系の位相幾何学的研究
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