2001 Fiscal Year Final Research Report Summary
Mathmatical study of complex systems
| Project/Area Number |
11837002
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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 Institution | Hokkaido University |
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Principal Investigator |
TSUJII Masato Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (20251598)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Makoto Nihon Univ., Fac. of Sci, Prof., 文理学部, 教授 (60092532)
KOMURO Motomasa Teikyo Science Univ., Fac. of Eng., Prof., 理工学部, 教授 (00186818)
TSUDA Ichiro Hokkaido Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (10207384)
MORITA Takehiko Hiroshima Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (00192782)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Complex system / Globally coupled maps / Piecewise expanding maps |
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| Research Abstract |
We study the dynamics of piecewise expanding maps in higher dimension. On the contrary to the one dimensional case, we show that a C^γ piecewise expanding map does not necessarily admit an absolutely continuous invariant measure. Also we show that if we assume that the map is piecewise analytic in 2dim or piecewise affine in higher dimension, it always admits an absolutely continuous invariant measure.
We also studied the so-called global lycoupled maps from a mathematical viewpoint. We made an extensive numerical experiment for 10 globally coupled logisitic map and came to the idea that the so-called "Chaotic inenerancy" in this case is caused by a hierarchy of on-off intermittencies on the invariant subspaces.
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