Project/Area Number  10440060 
Research Category 
GrantinAid for Scientific Research (B).

Section  一般 
Research Field 
Global analysis

Research Institution  KEIO UNIVERSITY 
Principal Investigator 
NAKADA Hitoshi KEIO UNIVERSITY, FACULTY OF SCIENCE AND TECHNOLOGY, PROFESSOR, 理工学部, 教授 (40118980)

CoInvestigator(Kenkyūbuntansha) 
ITO Yuji TOKAI UNIVERSITY, INSTITUTE OF EDUCATION, PROFESSOR, 教育開発研究所, 教授 (90112987)
森吉 仁志 慶應義塾大学, 理工学部, 助教授 (00239708)
菊池 紀夫 慶應義塾大学, 理工学部, 教授 (80090041)
SSHIOKAWA Iekata KEIO UNIVERSITY, FACULTY OF SCIENCE AND TECHNOLOGY, PROFESSOR, 理工学部, 教授 (00015835)
MAEDA Yoshiaki KEIO UNIVERSITY, FACULTY OF SCIENCE AND TECHNOLOGY, PROFESSOR, 理工学部, 教授 (40101076)
MAEJIMA Makoto KEIO UNIVERSITY, FACULTY OF SCIENCE AND TECHNOLOGY, PROFESSOR, 理工学部, 教授 (90051846)
ISHI Ippei KEIO UNIVERSITY, FACULTY OF SCIENCE AND TECHNOLOGY, ASSISTANT PROFESSOR, 理工学部, 助教授 (90051929)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥9,600,000 (Direct Cost : ¥9,600,000)
Fiscal Year 2000 : ¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1999 : ¥3,400,000 (Direct Cost : ¥3,400,000)
Fiscal Year 1998 : ¥3,400,000 (Direct Cost : ¥3,400,000)

Keywords  NONSINGULAR TRANSFORMATION / MARKOV SHIFT / MULTIPLE RECURRENCE / FORMAL POWER SERIES / 非特異エルゴード変換 / マルコフシフト / 多重再帰性 / 形式的べき級数 / II_∞型エルゴード変換 / dissipative sequence / upper Banach density / weakly wandering sequence / Zの直和分解 / Pascaladic変換 / 2次元ランドム・ウォーク / RogersRamanujan連分数展開 / II_∞型変換 / III_λ型変換 / Pascaladdic変換 / weakly mixing 
Research Abstract 
1. Multiplicity of recurrence of type II ∞ ergodic transformations : We classified the set of Markov shifts by the return sequence and also by KakutaniParry index. This result was appeared in a paper by J.Aaronson and H.Nakada, Israel Journal of Math. 2000. Moreover, Hamachi's research group has shown that the multiplicity of recurrence is preserved by the compact group extensions. 2. It has been known that the cardinality of the set of locally finite ergodic nvariant measures for a cylinder flow is continuous if the rotaion number of the base transformation is of bounded type. These measure are induced from the PL homeomorphisms of the circle, those were considered by Herman. In this project, we proved that there is no other locally finite invariant measure for such cylinder flows. On the other hand, we considered Maharam extensions of adding machines of Markovian type. We also determined the set of locally finite ergodic invariant measures for such Maharam extensions associated to Hoelder continuous potentials. 3. We studied continued fraction expansions of formal power series with a finite field coefficients. Moreover we considered the metrical theory of diopantine approximation in positive characteristic. We showed that analogue of some classical metric theorems hold. In particular, we proved the formal power series version of DufineSchaeffer thoerem.
