2011 Fiscal Year Final Research Report
Research on semigroups of holomorphic maps and random complex dynamics
| Project/Area Number |
21540216
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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, 大学院・理学研究科, 准教授 (40313324)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 複素力学系 / カオス / フラクタル幾何学 / ランダム力学系 / 複素解析学 / エルゴード理論 / ハウスドルフ次元 / 雑音誘起現象 |
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| Research Abstract |
I investigated the dynamics of semigroups of holomorphic maps on the Riemann sphere and the random complex dynamics on the Riemann sphere. I found many new phenomena which cannot hold in the usual iteration dynamics of a single holomorphic map. Moreover, I investigated those phenomena systematically. In particular,
I found that in random complex dynamics, for a generic system, the chaos of the averaged system disappears due to the automatic cooperation of many kinds of maps in the system(cooperation principle). Also, I investigated many complex phenomena of limit functions of the systems. Moreover, I investigated stability and bifurcation of the systems.
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