| Project/Area Number |
05452015
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
AOKI Nobuo Tokyo Metropolitan Univ.Faculty of Science, Professor, 理学部, 教授 (60087020)
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| Co-Investigator(Kenkyū-buntansha) |
平田 雅樹 東京都立大学, 理学部, 助手 (70254141)
MATSUI T Faculty of Science, Professor, 理学部, 助教授 (50199733)
NISHIOKA K Faculty of Science, Professor, 理学部, 助教授 (60101078)
YAMASHITA S Faculty of Science, Professor, 理学部, 助教授 (30087019)
TOMIYAMA J Faculty of Science, Professor, 理学部, 教授 (30006928)
HIRATA M Faculty of Science, Assistant Professor
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| Project Period (FY) |
1993 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1994: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1993: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | chaos / sensitive / manifold / dynamical system / prediction / 現象 / 沈点 / 源点 / 環 / 半群 / エルゴード |
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| Research Abstract |
Lorenz in his remarble work on the dynamical modelling of weather prediction stressed implying that some degree of uncertainty of such a prediction is unavoidable and no matter how accurate are the initial data.
On the work of Lorenz it can be seen that chaotic behavior of a system with respect to initial condition was introduced in the area of dynamical systems theory. Usually, a dynamical system is given as a transformation on a space of events. This space of events can be a manifold.
Concerning dynamical systems on a manifold, an interesting problem is posed as follows :
"Are the diffeomorphisms with axiom A C^1-dense in the space of all surface diffeomorphisms? "
Our project could give an answer for this important problem.
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