2013 Fiscal Year Final Research Report
Research on parameter spaces in complex dynamics
| Project/Area Number |
22740105
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
INOU Hiroyuki 京都大学, 理学(系)研究科(研究院), 講師 (00362434)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 複素力学系 / Mandelbrot集合 |
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| Research Abstract |
Computer pictures has been playing an important role in studying complicated phoenomena in complex dynamics. Recent development in computer envirionment and virtual reality technology enabled us to immerse into 3D virtual reality space. We visualize objects in complex 2D (real 4D) space with help of such a technology.
We proved that homeomorphic copies of Mandelbrot set and so on are naturally embedded into 1-parameter spaces of cubic polynomials with a periodic critical points.
We proved that the tricorn, an analogue of the Mandelbrot set in the anti-holomorphic quadratic family does not have the self-similar property which the Mandelbrot set has.
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