2001 Fiscal Year Final Research Report Summary
Research on ergodic theory and Perron-Frobenius operator
| Project/Area Number |
12640190
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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 |
Basic analysis
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| Research Institution | Nihon University |
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Principal Investigator |
MORI Makoto Dept. Math. CHS. Nihon University, Professor, 文理学部, 教授 (60092532)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUDA Takuo Dept. Math. CHS. Nihon University, Professor, 文理学部, 教授 (00009599)
WATANABE Keiichi Dept. Math. CHS. Nihon University, Professor, 文理学部, 教授 (10087083)
KURODA Koji Dept. Math. CHS. Nihon University, Professor, 文理学部, 教授 (50153416)
YAMAURA Yoshihiko Dept. Math. CHS. Nihon Univ., Associate Prof., 文理学部, 助教授 (90255597)
SUZUKI Osamu Dept. Math. CHS. Nihon University, Professor, 文理学部, 教授 (10096844)
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| Project Period (FY) |
2000 – 2001
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| Keywords | ergodic theory / Perron-Frobenius Operator / fractal / random number / Brownian motion |
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| Research Abstract |
We have constructed low discrepancy sequences using dynamical system. Our main tool is the spectra of the Perron-Frobenius operator associated with the dynamical system.
We calculate the Hausdorff dimensions of the fractals generated by dynamical systems, and at the same time we study the ergodic properties of the dynamical system on fractals. We studied a phase transition of a one parameter family of fractals.
Using random walks generated by dynamical systems, we construct a Brownian motion and calculate the order of convergence.
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Research Products
(13 results)
