| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
In this research project, we consider the sets of diffeomorphisms which are measure-expansive for any probability measure, invariant probability measure and ergodic measure, and study the sets from the viewpoint of geometric theory of dynamical systems.
It is proved that the C1-interior of the set of measure-expansive diffeomorphisms for any probability measure is quasi-Anosov systems and C1-interior of the set of measure-expansive diffeomorphisms for any invariant probability measures is Ω-stable systems. Furthermore, it is also proved that there exists a non-empty C1-open set of robustly non-hyperbolic and transitive diffeomorphisms such that each element of the set is measure expansive for any ergodic measure.
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