论文标题
Lebesgue测量保存汤普森的单型
Lebesgue Measure Preserving Thompson's Monoid
论文作者
论文摘要
本文定义了Lebesgue Measure保存汤普森的单体，用$ \ mathbb {g} $表示，该$在汤普森的$ \ mathbb {f} $上建模，除了$ \ mathbb {g} $的元素是不可简化的。此外，要求$ \ mathbb {g} $保存lebesgue度量的元素。 MONOID $ \ MATHBB {G} $与Thompson的Group $ \ Mathbb {f} $具有截然不同的属性。本文研究了$ \ mathbb {g} $的许多代数（组理论）和动力学特性，包括近似，混合，周期性，熵，分解，发电机和拓扑结合。
This paper defines Lebesgue measure preserving Thompson's monoid, denoted by $\mathbb{G}$, which is modeled on Thompson's group $\mathbb{F}$ except that the elements of $\mathbb{G}$ are non-invertible. Moreover, it is required that the elements of $\mathbb{G}$ preserve Lebesgue measure. Monoid $\mathbb{G}$ exhibits very different properties from Thompson's group $\mathbb{F}$. The paper studies a number of algebraic (group-theoretic) and dynamical properties of $\mathbb{G}$ including approximation, mixing, periodicity, entropy, decomposition, generators, and topological conjugacy.
