A typical dynamical system is not simple or semisimple
A typical dynamical system is not simple or semisimple
复制标题
典型的动力系统并不简单或半简单
DOI：
--
复制
发表时间：
2003
影响因子：
0.9
通讯作者：
O. Ageev
中科院分区：
文献类型：
--
作者：
O. Ageev
我们研究了标准非原子Borel空间$(X，MU)$的典型变换的二重自结合的结构。我们证明了典型的自同构不是简单和半单的。这是对德尔琼科、鲁道夫、莱曼日克和门岑提出的问题的回答。为了回答这些问题，我们证明了对于一个典型的变换，存在集中在两个纤维上的遍历自联接，即存在最简单的非平凡的遍历自联接。
We study the structure of two-fold self-joinings for a typical transformation of the standard non-atomic Borel space $(X,mu)$. We prove that the typical automorphism is not simple and semisimple. This is an answer to questions posed by del Junco, Rudolph, Lemanczyk and Mentzen. In order to answer these questions we proved that for a typical transformation there exists an ergodic self-joining concentrated on two fibers, i.e. there exists the simplest non-trivial ergodic self-joining.