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 fype II∞Ergodic变换的复发性多样性：我们按回报序列以及Kakutani-Parry索引对Markov偏移进行了分类。该结果出现在以色列数学杂志的J.Aaronson和H.Nakada的论文中。 2000年。此外，哈马奇的研究小组表明，紧凑型组扩展可以保留复发的多样性。2。众所周知，如果基本转换的转换数为有界类型，则局部有限的Ergodic NVariant措施的基数是连续的。这些测量是从圆圈的PL同构形态学引起的，这些测量是由赫尔曼考虑的。在这个项目中，我们证明了此类圆柱流没有其他本地有限的不变措施。另一方面，我们考虑了添加Markovian类型机器的Maharam扩展。我们还确定了与Hoelder持续电势相关的此类Maharam扩展的局部有限的千古不变措施。3。我们研究了具有有限场系数的正式功率系列的持续扩展。此外，我们考虑了阳性特征中的二翼反反式的度量理论。我们展示了某些经典定理的类似物。特别是，我们提供了Dufine-Schaeffer Thoerem的正式Power Series版本。