| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
We studied geometric criteria for the ergodicity of volume preserving dynamical systems. It is widely known that the Hopf argument is a simple but strong method in the ergodic theory of Anosov systems. For a broader class of dynamical systems, called the non-uniformly hyperbolic systems, we extend the method under an assumption on the dimension of the phase space or the associated foliations. As an application, we showed that the ergodicity on every closed three-manifold follows from a topological property of the system. Further, it has turned out that every topological transitive topological Anosov system is ergodic.
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