| Project/Area Number |
09640261
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
YOSHIHARA Hideaki Kyoto Univ., Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (10182809)
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| Co-Investigator(Kenkyū-buntansha) |
OKA Hiroe Ryukoku Univ., Faculty of Science and Technology Professor, 理工学部, 教授 (20215221)
NISHIURA Yasumasa Hokkaido Univ., Research Institute for Electronic Sciences Professor, 電子科学研究所, 教授 (00131277)
OKAMOTO Hisashi Kyoto Univ., Research Institute of Mathematical Sciences Professor, 大学院・数理解析研究所, 教授 (40143359)
USHIKI Shigehiro Kyoto Univ., Graduate School of Human and Environmental Studies, Professor, 大学院・人間環境学研究, 教授 (10093197)
NISHIDA Takaaki Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70026110)
三波 篤郎 北見工業大学, 工学部, 教授 (30154157)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | dynamical system / bifurcation / global structure / structural stability / hyperbolicity / singular perturbation / topological index / pattern / 数値的検証 |
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| Research Abstract |
The following results have been obtained in this research project :
1. Study of non-hyperbolic dynamical systems, in particular, a result toward Palis conjecture that aims at describing dynamical structures for a dense set of dynamical systems in C^1 topology (Hayashi)
2. Complex dynamical systems and hyper functions in relation to ergodic theory, in particular the Ruelle operator (Ushiki)
3. Existence and statistical properties of absolutely continuous invariant measures in two dimensional real analytic and higher dimensional piecewise linear expanding maps (Tsujii)
4. Conley index theory for singularly perturbed vector fields of slow-fast type in the case of one-dimensional slow dynamics (Oka)
5. Monotonicity of topological entropy for piecewise-linear symmetric bimodal maps (Oka)
6. Analytic and computer assisted approach to global bifurcation phenomena in the Rayleigh-Benard problem, in particular a new method for proving the existence of solutions for various different parametres using the validated numerical computation (Nishida and Yoshihara)
7. Blow-up of solutions in the Proudman-Johnson equation (Okamoto)
8. Analytical and dynamical investigation of self-replicating patterns which describe new spatial patterns observed in real chemical and biological experiments (Nishiura)
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