2012 Fiscal Year Final Research Report
Dynamics on algebraic varieties and Painleve equations
| Project/Area Number |
20340036
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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 | Hokkaido University (2010-2012)
Kyushu University (2008-2009) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
UEHARA Takato 新潟大学, 自然科学系, 助教 (40613261)
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| Co-Investigator(Renkei-kenkyūsha) |
KAJIWARA Kenji 九州大学, MI研究所, 教授 (40268115)
KAMIMOTO Joe 九州大学, 大学院・数理学研究院, 准教授 (90301374)
TSUJII Masato 九州大学, 大学院・数理学研究院, 教授 (20251598)
ISHII Yutaka 九州大学, 大学院・数理学研究院, 准教授 (20304727)
TSUDA Teruhisa 一橋大学, 大学院・経済学研究科, 准教授 (00452730)
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| Project Period (FY) |
2008 – 2012
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| Keywords | パンルヴェ方程式 / 力学系 / リーマン / ヒルベルト対応 / 指標多様体 / モデュライ空間 / エルゴード理論 / カオス / 周期点 |
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| Research Abstract |
We developed a dynamical study of the sixth Painleve equation on the algebro-geometrical and moduli theoretical foundations of the Painleve system. When the parameter lies on the walls of an affine Weyl group, we established the chaotic nature of the system and proved the exponential growth of the number of isolated periodic solutions. To obtain these results, we developed a general theory of periodic points for area-preserving birational maps on a projective surface. Constructing rational surface automorphisms of positive entropy has also been discussed.
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