权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

On a clacification problem of type II ∞ and type III ergodic transformations and its application

关于II型∞和III型遍历变换的澄清问题及其应用

基本信息

批准号：
10440060
负责人：
NAKADA Hitoshi
金额：
$ 6.14万
依托单位：
KEIO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440060/
关键词：
NONSINGULAR TRANSFORMATION MARKOV SHIFT MULTIPLE RECURRENCE FORMAL POWER SERIES II_∞型エルゴード変換 dissipative sequence upper Banach density weakly wandering sequence Zの直和分解 Pascal-adic変換 2次元ランドム・ウォーク Rogers-Ramanujan連分数展開 II_∞型変換 III_

项目摘要

1. Multiplicity of recurrence of type II ∞ ergodic transformations : We classified the set of Markov shifts by the return sequence and also by Kakutani-Parry 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 Dufine-Schaeffer thoerem.

1. II型∞遍历变换的常返性的多重性：我们通过返回序列和Kakutani-Parry指标对马尔可夫移位集进行了分类。这个结果发表在J.Aaronson和H.Nakada的论文中，Israel Journal of Math.2000。此外，Hamachi的研究小组已经证明了递归的多重性被紧群扩张所保持。已知柱流的局部有限遍历不变测度集的基数是连续的，如果基变换的旋转数是有界型的。这些测度是由赫尔曼所考虑的圆的PL同胚导出的。在这个项目中，我们证明了没有其他的局部有限不变的措施，这样的圆柱流。另一方面，我们考虑了马尔可夫型加法机的Maharam扩展。我们还确定了与Hoelder连续势相关的Maharam扩张的局部有限遍历不变测度集.研究了有限域系数形式幂级数的连分式展开式。此外，我们考虑了度规理论的正特征。我们证明了一些经典度量定理的类比成立。特别地，我们证明了Dufine-Schaeffer定理的形式幂级数形式。