Research on the bifurcation and renormalization of dynamical systems
Project/Area Number |
22340033
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Research Category |
Grant-in-Aid for Scientific Research (B)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Global analysis
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Research Institution | Kyoto University |
Principal Investigator |
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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)
稲生 啓行 京都大学, 理学(系)研究科(研究院), 講師 (00362434)
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Co-Investigator(Renkei-kenkyūsha) |
INOU Hiroyuki 京都大学, 大学院理学研究科, 講師 (00362434)
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Project Period (FY) |
2010-04-01 – 2015-03-31
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Project Status |
Completed (Fiscal Year 2014)
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Budget Amount *help |
¥16,510,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥3,810,000)
Fiscal Year 2013: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
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Keywords | 力学系 / カオス / フラクタル / 分岐 / くりこみ / ジュリア集合 / 複素力学系 / 放物型不動点 / 剛性 |
Outline of Final Research Achievements |
We studied the bifurcation of chaotic dynamical systems, especially low dimensional complex dynamical systems. In order to study the bifurcation of parabolic or semi-parabolic fixed points, we established the theory of parabolic and near-parabolic renormalization, and found an invariant space of functions under these renormalizations. We introduced the notion of dynamical charts, and combining the invariant space of near-parabolic renormalization, we studied the dynamical properties and invariant sets (called hedgehogs) near irrationally invariant fixed points. We also studied the local structure and the bifurcation of semi-parabolic fixed point of two-dimensional holomorphic mappings, and obtained results on the continuity and discontinuity of the parabolic/attracting basins and unstable manifolds.
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Report
(5 results)
Research Products
(45 results)
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[Presentation] 複素力学系の問題2010
Author(s)
宍倉光広
Organizer
複素幾何学の諸問題
Place of Presentation
京都大学数理解析研究所(招待講演)
Year and Date
2010-09-06
Related Report
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