2011 Fiscal Year Final Research Report
Elucidation of the boundary of various Siegel disks influenced by continued fraction expansions
| Project/Area Number |
21740121
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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 | Ichinoseki National College of Technology |
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Principal Investigator |
KATAGATA Koh 一関工業高等専門学校, 一般教科自然科学系, 講師 (10529598)
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| Research Collaborator |
NAKANISHI Toshihiro 島根大学, 総合理工学部, 教授 (00172354)
ONITSUKA Masakazu 都城工業高等専門学校, 一般科目, 講師 (20548367)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 複素力学系 / ジーゲル円板 / 連分数展開 |
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| Research Abstract |
2009y : We obtained that for some transcendental entire functions,"the boundary of Siegel disks whose rotation number was of bounded type was a quasicircle". We obtained that the logarithmic lift of these transcendental entire functions had a wandering domain whose boundary was a quasicircle as a corollary.
2010y : We constructed some transcendental entire functions satisfying that "the boundary of Siegel disks whose rotation number was of bounded type was a quasicircle". We introduced a topology on the set of all entire functions respecting dynamics and we studied variation of Siegel disks for small perturbation with respect to the topology.
2011y : We comprehended the relationship between the qualitative theory of differential equations and complex dynamics, and we studied that(super) attracting periodic points, parabolic periodic points, Siegel points and Cremer points for complex dynamics and equilibrium points for differential equations.
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