| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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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