Laminations in complex dynamics generated by Zalcman's lemma
| Project/Area Number |
24740103
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Tokyo Institute of Technology (2014-2015)
Nagoya University (2012-2013) |
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Principal Investigator |
Kawahira Tomoki 東京工業大学, 理工学研究科, 准教授 (50377975)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 複素力学系 / ザルクマンの補題 / ラミネーション / 剛性 / Zalcmanの補題 / 力学系の剛性 / Mandelbrot集合 / Julia集合 / Tricorn / Julia 集合 / Teichmuller理論 / 国際情報交換 / タイヒミュラー理論 |
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| Outline of Final Research Achievements |
A complex dynamics is a system where the complex numbers move according to a deterministic law of motion. We mainly considered the cases when the law of motion depends on a complex parameter. The system may be unstable under perturbation at some parameters and the set of such parameters often behaves like a chaotic locus of a given complex dynamics. In this research project, we choose "Zalcman's lemma" as a bridge that connects dynamical systems and the parameter spaces. Most of our results are related to the family of quadratic polynomials.
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Report
(5 results)
Research Products
(19 results)
