1995 Fiscal Year Final Research Report Summary
Research on ergodic theory and its applications
Project/Area Number 
06452017

Research Category 
GrantinAid for General Scientific Research (B)

Allocation Type  Singleyear Grants 
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) 
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)

Project Period (FY) 
1994 – 1995

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 
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.

Research Products
(12 results)