Research on holomorphic mappings semigroups, random complex dynamical systems and fractal geometry
| Project/Area Number |
15K04899
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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 |
Basic analysis
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| Research Institution | Kyoto University (2017)
Osaka University (2015-2016) |
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Principal Investigator |
Sumi Hiroki 京都大学, 人間・環境学研究科, 教授 (40313324)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| 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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| Keywords | ランダム複素力学系 / フラクタル幾何学 / 正則写像半群 / ジュリア集合 / エルゴード理論 / マルチフラクタル解析 / 複素特異関数 / 複素解析学 / 等角反復関数系 / 複素力学系 / 有理半群 / フラクタル / ランダム力学系 / ランダム性誘起現象 / マルコフ過程 |
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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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Report
(4 results)
Research Products
(52 results)
