Research on random complex dynamics and the dynamics of semigroups of holomorphic maps
| Project/Area Number |
24540211
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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 | Osaka University |
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Principal Investigator |
SUMI Hiroki 大阪大学, 理学(系)研究科(研究院), 准教授 (40313324)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Yuzuru 北海道大学, 電子科学研究所, 准教授 (30342794)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 複素力学系 / ランダム複素力学系 / フラクタル / エルゴード理論 / 協調原理 / ジュリア集合 / 複素解析 / 有理半群 / 多項式半群 / 有理半群 アメリカ / カオス / 反復関数系 / 複素特異関数 / 乱雑性誘起現象 / フラクタル幾何学 / ハウスドルフ次元 / 横断性条件 |
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| Outline of Final Research Achievements |
I investigated the random dynamics of rational maps and the dynamics of semigroups of rational maps on the Riemann sphere. I showed that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere, due to the automatic cooperation of the generators. I investigated the iteration and spectral properties of transition operators acting on the space of (Hoelder) continuous functions on the Riemann sphere. I showed that the set of stable systems is open and dense in the space of random dynamical systems of polynomials. Also, I investigated the limit state functions. By taking a partial derivative of the function of probability of tending to a minimal set with respect to a probability parameter, I introduced a complex analogue of the Takagi function. I am developing multifractal analysis for limit state funtions and the complex analogue of the Takagi function.
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Report
(4 results)
Research Products
(49 results)
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[Presentation] Random basin in dice roll2014
Author(s)
Yuzuru Sato
Organizer
Workshop on Theory and Applications of Random/Non-autonomous Dynamical Systems
Place of Presentation
Imperial College London, London, UK
Year and Date
2014-09-11
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