| Project/Area Number |
19540085
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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 |
Geometry
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| Research Institution | Shimane University |
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Principal Investigator |
YOKOI Katsuya Shimane University, 医学部, 教授 (90240184)
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| Co-Investigator(Kenkyū-buntansha) |
HOSAKA Tetsuya 宇都宮大学, 教育学部, 准教授 (50344908)
KIMURA Makoto 島根大学, 総合理工学部, 教授 (30186332)
HATTORI Yasunao 島根大学, 総合理工学部, 教授 (20144553)
FURUMOCHI Tetsuo 島根大学, 総合理工学部, 教授 (40039128)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 位相幾何学 / 位相的力学系 / 次元論 / 鎖回帰集合 / 周期 / 力学系 / 不動点 / 差分方程式 / 鎖回帰性 / 周期解 / 周期点 / 理想境界 / 位相力学系 / アトラクター / コンパクト距離空間 |
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| Research Abstract |
We considered the dynamical behavior of maps on graphs, compacta with good local property. Main results are the following : (1) We established a Barge-Martin type theorem for graph self-maps for which the set of periodic points is dense. (2) For a self-map of a compactum we gave a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points. (3) Given an n-dimensional locally (n-1)-connected compact space X (n>=1) and a finite Borel measure μwithout atoms at isolated points, we proved that for a generic map f : X -> X, the set of points which are chain recurrent under f has μ-measure zero.
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