2012 Fiscal Year Final Research Report
Study of foliations and discrete group actions
| Project/Area Number |
20540096
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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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| Co-Investigator(Renkei-kenkyūsha) |
NAKAYAMA Hiromichi 青山学院大学, 理工学部, 教授 (30227970)
INABA Takashi 千葉大学, 自然科学研究科, 教授 (40125901)
MITSUMATSU Yoshihiko 中央大学, 理工学部, 教授 (70190725)
KODAMA Hiroki 東京大学, 数理科学研究科, 特任助教 (40466826)
TSUBOI Takashi 東京大学, 数理科学研究科, 教授 (40114566)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 葉層構造 / 群作用 |
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| Research Abstract |
Assume that a homeomorphism of the plane admits a compact minimal set which is connected and not a point. We showed that there are exactly two invariant connected components of the complement. We also showed that the rotation number is uniquely determined. Given a foliation on a compact manifold and a leafwise Riemannian metric, there is defined a harmonic measure of the manifold. In case the metric is hyperbolic and the harmonic measure is ergodic, we showed that there is a dichotomy of the measures. Among flows along the Reeb foliation of the plane, there is one which is called standard. We characterized it by its dynamical property.
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Research Products
(16 results)
