Large deviation principle and multifractal analysis in dynamical systems
| Project/Area Number |
24540212
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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 | Hiroshima University |
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Principal Investigator |
Chung Yong Moo 広島大学, 工学(系)研究科(研究院), 准教授 (20314734)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKAHASI Hiroki 慶應義塾大学, 理工学部, 准教授 (00467440)
SUMI Naoya 熊本大学, 自然科学研究科, 教授 (50301411)
MIKAMI Toshio 津田塾大学, 学芸学部, 教授 (70229657)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 力学系 / 大偏差原理 / マルチフラクタル / 可微分力学系 / マルチフラクタル解析 / 力学系理論 |
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| Outline of Final Research Achievements |
We obtained a criterion to hold the large deviation principle for smooth dynamical systems on the interval. If a multimodal map without flat critical points has the following properties: (1) the exponential growth of the derivative on the set of critical values with respect to the time evolution; (2) the sub-exponential slow recurrence of the critical orbits; (3) the topological exactness, the large deviation principle of level 2 holds. From our result it is shown that almost every stochastic quadratic map satisfies the large deviation principle. Moreover we gave a representation of the Birkhoff spectrum by using thermodynamic formalism, and showed its continuity.
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Report
(5 results)
Research Products
(40 results)
