2013 Fiscal Year Final Research Report
Fixed points and critical points in higher dimensional complex dynamics
| Project/Area Number |
21540176
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
UEDA Tetsuo 京都大学, 理学(系)研究科(研究院), 教授 (10127053)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 複素力学系 / 放物型不動点 / ジュリア集合 / インプロージョン / 分岐点 / ファトゥ集合 |
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| Research Abstract |
I studied complex dynamics in higher dimension from the point of view of complex analysis of several complex variables. In particular, I investigated the phenomenon of implosion, i.e., the discontinuous change of (filled) Julia set that occur when a semi-parabolic and semi-attracting fixed point of a Henon mapping is perturbed. Also I investigated the dynamics of holomorphic self mappings of complex projective spaces. By tracking the orbit of the critical set, I obtained the condition for the set of repelling periodic points is dense in the projective space.
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