2005 Fiscal Year Final Research Report Summary
Analysis on a fractal set and Iteration dynamical systems of discrete Laplacians
| Project/Area Number |
16540122
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nihon University |
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Principal Investigator |
SUZUKI Osamu Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (10096844)
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| Co-Investigator(Kenkyū-buntansha) |
NONO Kiyoharu Fukuoka University of Education, Faculty of Education, Professor, 教育学部, 教授 (10117046)
MORI Makoto Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (60092532)
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| Project Period (FY) |
2004 – 2005
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| Keywords | discrete Laplacian / iteration dynamical system / fractal set / organization and evolution |
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| Research Abstract |
System analysis is performed in the case of (1)Iteration dynamical systems of discrete Laplacian and (2)Differential and integral calculus on a fractal sets. Details can be described in the cases separately :
(1)Iteration dynamical systems of discrete Laplacian
The laplacian operator plays a very important role in mathematical physics. We may say that we can describe nothing without the Laplacian operator. Hence we may try to discretize Laplacian operators and consider the iteration dynamical systems. In this research we propose the idea on the description of the organizations and evolutions. In fact, we can give a systematic description of the designs of carpets, laces and embroideries. Also we can describe the evolutions of the extinct animals. Here we want to make a stress on the fact that we can describe the mass extinctions quite well.
(2)Differential and integral calculus on a fractal set.
We have a quite natural invariant measure on a fractal set and we can develop the integral theory with respect to the measure. In this research we could introduce derivations on a fractal set and then we can develop the differential and integral calculus on a fractal set.
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