| 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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| 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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