2015 Fiscal Year Final Research Report
On the characterization of measure-expansive differentiable dynamical systems
| Project/Area Number |
25400105
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Utsunomiya University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 力学系理論 / 拡大性 / 確率測度 / 双曲性 / 占有的分解 |
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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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| Free Research Field |
擬軌道尾行性や拡大性を持つ力学系の特徴付け
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