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 |
MATSUMOTO Shigenori (2010) Nihon University, 理工学部, 教授 (00601433)
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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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 葉層構造 / 群作用 / 円周上の微分可能同窓写像 / 回転数 / Liouville 数 / 離散群作用 / 平面写像 / 連続体 / prime end / Liouville数 / ヘルダー連続 / 絶対連続 / 離散群 / 多様体 / エルゴード性 / 極小集合 / 基本領域 / 不変測度 / パラメータ剛性 / Diophantus条件 / 調和測度 / 特異測度 / 力学系 / 流れ / リー群 / 剛性 |
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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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Report
(7 results)
Research Products
(33 results)
