标题： 勒贝格测度保持汤普森独异点 显示英文标题

标题： Lebesgue Measure Preserving Thompson's Monoid

摘要： 本文定义了保勒贝格测度的汤普森独异点，记为$\mathbb{G}$，它以汤普森群$\mathbb{F}$为模型，只是$\mathbb{G}$的元素是不可逆的。 此外，要求$\mathbb{G}$的元素保持勒贝格测度。 独异点$\mathbb{G}$展现出与汤普森群$\mathbb{F}$截然不同的性质。 本文研究了$\mathbb{G}$的一些代数（群论）和动力学性质，包括逼近性、混合性、周期性、熵、分解、生成元和拓扑共轭。 显示英文摘要

摘要： 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.