2013 Fiscal Year Final Research Report
Study of probability density for the existence of orbits
| Project/Area Number |
23540234
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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 |
Global analysis
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| Research Institution | Kumamoto University (2013)
Tokyo Institute of Technology (2011-2012) |
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Principal Investigator |
SUMI Naoya 熊本大学, 自然科学研究科, 教授 (50301411)
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| Co-Investigator(Renkei-kenkyūsha) |
HIRAYAMA Michihiro 九州工業大学, 工学研究科, 准教授 (50452735)
MORIYASU Kazumine 徳島大学, ソシオ・アーツ・アンド・サイエンス研究部, 教授 (60253184)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 解析学 / 力学系 / エルゴード理論 |
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| Research Abstract |
We study some technique for deriving global properties of probability density for the existence of orbits from local conditions on the behaviors of pairwise disjoint orbits. In particular, we show the following result for some dynamical systems: if for every pair of orbits, there exists another orbit which transfers from one orbit to the other, then (1) the probability density for the existence of orbits is uniquely determined, and (2) one can estimate the difference between the probability density for the existence of finite orbit and that of infinite orbit, by using the entropy and the potential.
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