| Project/Area Number |
15K04902
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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 | Kumamoto University |
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Principal Investigator |
Sumi Naoya 熊本大学, 大学院先端科学研究部(理), 教授 (50301411)
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| Research Collaborator |
HIRAYAMA Michihiro 筑波大学, 数理物質科学研究科, 准教授 (50452735)
CHUNG Yong Moo 広島大学, 工学研究科, 准教授 (20314734)
YAMAMOTO Kenichiro 長岡技術科学大学, 工学部, 准教授 (30635181)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 解析学 / 力学系 / エルゴード理論 |
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| Outline of Final Research Achievements |
In this study, we proved that in the case when the ambient space is at most 3-dimensional, under the local condition that for every pair of orbits, there exists another orbit which transfers from one orbit to the other, the following global dynamical property holds: if the density function for the existence probability of orbits exists for every orbit, then it is uniquely determined. Moreover, if the dynamical system satisfies the specification property, we obtained a similar result.
On the other hands, concerning the space of all dynamical systems satisfying the specification property, the following holds: if a partially hyperbolic diffeomorphism has two saddles with different indices, and the central direction is one-dimensional, then it does not satisfy the specification property.
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| Academic Significance and Societal Importance of the Research Achievements |
軌道の存在状態を表す確率密度は，力学系理論の初期から扱われている基本的な研究対象である．存在確率密度の一意性は，力学系が個々の軌道に依らない１つの平衡状態をもつことを保証する．本研究により，相空間の次元が3次元以下の場合に，平衡状態の一意性という大域的な性質は，局所的な軌道同士の条件から導かれることが結論付けられた．
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