2009 Fiscal Year Final Research Report
Complex analytic study of real and complex dynamical systems
| Project/Area Number |
18340048
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
SHISHIKURA Mitsuhiro Kyoto University, 大学院・理学研究科, 教授 (70192606)
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| Co-Investigator(Kenkyū-buntansha) |
UEDA Tetsuo 京都大学, 大学院・理学研究科, 教授 (10127053)
KOKUBU Hiroshi 京都大学, 大学院・理学研究科, 教授 (50202057)
INOU Hiroyuki 京都大学, 大学院・理学研究科, 講師 (00362434)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUJII Masato 九州大学, 大学院・数理学研究院, 教授 (20251598)
TANIGUCHI Masahiko 奈良女子大学, 理学部, 教授 (50108974)
ITO Hidekazu 金沢大学, 数物科学系, 教授 (90159905)
ARAI Zin 北海道大学, 創成研究機構, 特認助教 (80362432)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 力学系 / くりこみ / 分岐現象 / ジュリア集合 / カオス / フラクタル / タイヒミュラー空間 / 構造安定性 |
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| Research Abstract |
We studied the structure of invariant sets and bifurcation phenomena of real and complex dynamical systems via complex analytic methods. For irrationally indifferent fixed points of one-dimensional complex dynamical systems, we defined near-parabolic renormalization and constructed its invariant space of functions. This space was shown to correspond to the Teichmueller space of once-punctured disk and the renormalization is contracting with respect to the Teichmueller metric.
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