2014 Fiscal Year Final Research Report
Absolute continuity of foliations and ergodicity for smooth measure preserving partially hyperbolic dynamics
| Project/Area Number |
24740105
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | University of Tsukuba (2014)
Kyushu Institute of Technology (2012-2013) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | エルゴード性 |
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| Outline of Final Research Achievements |
We studied geometric criteria for the ergodicity problem in smooth dynamical systems. It is known that the so-called Hopf argument is a simple but strong method in the ergodic theory of Anosov systems. We extended the Hopf argument for Anosov systems to a broad class of dynamical systems, the non-uniformly hyperbolic systems, and constructed a geometric structure which yields the ergodicity. One of the differences between these dynamics is that while the foliations of Anosov systems do have transverse intersections, while the foliations of the non-uniformly hyperbolic systems may have tangential points. As an application, we got another proof of the ergodicity of transitive non-uniformly hyperbolic surface diffeomorphisms. Further, we constructed a non-empty open set in the space of partially hyperbolic systems of which the ergodicity is a dense phenomenon.
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| Free Research Field |
力学系理論，エルゴード理論
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