| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
I investigated the dynamics of semigroups of holomorphic maps on the Riemann sphere and random holomorphic dynamical systems. Also, I investigated fractals and fractal functions which appear in the limit states of such systems. The details are as follows.(1)I obtained many results on the parameter space of 2-generator semigroups.(2)I showed the Bowen's formula for (pre) Julia sets of expanding infinitely generated semigroups.(3)Regarding random holomorphic dynamical systems, I investigated the limit state functions and the partial derivatives of them with respect to probability parameters, and I obtained some results on the pointwise Hoelder exponents of such functions and the related multifractal analysis.(4)I investigated random dynamical systems generated by probability measures on analytic families of rational maps. I showed that generic such systems have weak stability, and applied the theory to investigate random relaxed Newton's methods to find roots of any polynomial.
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