Project/Area Number  06452017 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Keio University 
Principal Investigator 
ITO Yuji Keio Univ., Math.Dep't Professor, 理工学部, 教授 (90112987)

CoInvestigator(Kenkyūbuntansha) 
ENOMOTO Hikoe Keio Univ., Math.Professor, 理工学部, 教授 (00011669)
MAEDA Yoshiaki Keio Univ., Math.Professor, 理工学部, 教授 (40101076)
TANAKA Hiroshi Keio Univ., Math.Professor, 理工学部, 教授 (70011468)
SHIOKAWA Iekata Keio Univ., Math.Professor, 理工学部, 教授 (00015835)
NAKADA Hitoshi Keio Univ., Math.Assoc.Prof., 理工学部, 助教授 (40118980)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

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)

Keywords  type II^* & III transformations / RadonNikodym cocycles / exhaustive weakly wandering sequences / direct sum decompostion of 2 / multiple recurrence / KakutaniParry index / cutting and stacking method / complexity of sequences / II∞型及びIII型エルゴード的変換 / ラドン.ニコディム・コサイクル / 整数集合Zの直和分解 / exhanstive weably wandering seq / 多重再帰定理 / cntting and stacking構成法 / 符号別のComplexity / 剛性定理 / 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 
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 (socalled typ II_* and type III transformations) were investigated in depth. In particular, asymptotic behavior of the RadonNikodym 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 KakutaniParry index was established. 2. Concerning the interrelation between ergodic theory and othe areas, complexity of th esymbolic sequences associated with 3dimensional billiard was determined, and sharp L^*norm estimates for eigen functions for Laplacian on hyperbolic 3 manifolds were obtained.
