Research on ergodic theory and its applications
| Project/Area Number |
06452017
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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 | Keio University |
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Principal Investigator |
ITO Yuji Keio Univ., Math.Dep't Professor, 理工学部, 教授 (90112987)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOKAWA Iekata Keio Univ., Math.Professor, 理工学部, 教授 (00015835)
MAEDA Yoshiaki Keio Univ., Math.Professor, 理工学部, 教授 (40101076)
ENOMOTO Hikoe Keio Univ., Math.Professor, 理工学部, 教授 (00011669)
TANAKA Hiroshi Keio Univ., Math.Professor, 理工学部, 教授 (70011468)
NAKADA Hitoshi Keio Univ., Math.Assoc.Prof., 理工学部, 助教授 (40118980)
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| Project Period (FY) |
1994 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| Budget Amount *help |
¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 1995: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1994: ¥3,900,000 (Direct Cost: ¥3,900,000)
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| Keywords | type II^* & III transformations / Radon-Nikodym cocycles / exhaustive weakly wandering sequences / direct sum decompostion of 2 / multiple recurrence / Kakutani-Parry index / cutting and stacking method / complexity of sequences / II_∞型及びIII型エルゴード変換 / ラドン・ニコディム・コサイクル / exhaustive weakly wandering seq. / 多重再帰性 / cutting and stacking構成法 / 符号列のComplexity / II_∞型エルゴード変換 / Zの直和分解 / Gauss数体上の連分数近似 / 3次元ビリヤードの符号列 / 量子的エルゴード性 / ブラウン媒質内の拡散過程 / 自己相似過程 / 局所誘導方程式 |
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| Research Abstract |
In this project, researches concerning diversified areas connected with ergodic theory were carried out by a number of mathematicians working in the areas of ergodic theory, probability theory, functional analysis, analytic number theory, combinatorics and differential geometry, and many significant results were obtained.
1. In ergodic theory proper, properties of ergodic transformations which are characteristic for transformations having no finite invariant measures (so-called typ II_* and type III transformations) were investigated in depth. In particular, asymptotic behavior of the Radon-Nikodym cocycles and properties of exhaustive weakly wandering sequences and their relation to the direct sum decomposition of the integers Z were studied and a number of interesting results were obtained. Furthermore, multiple recurrence properties of type II_* transformations were studied and their relation with Kakutani-Parry index was established.
2. Concerning the interrelation between ergodic theory and othe areas, complexity of th esymbolic sequences associated with 3-dimensional billiard was determined, and sharp L^*-norm estimates for eigen functions for Laplacian on hyperbolic 3 manifolds were obtained.
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Report
(3 results)
Research Products
(41 results)
