• Corpus ID: 222090093

Lebesgue Measure Preserving Thompson's Monoid

  title={Lebesgue Measure Preserving Thompson's Monoid},
  author={William Li},
  journal={arXiv: Dynamical Systems},
  • William Li
  • Published 1 October 2020
  • Mathematics
  • arXiv: Dynamical Systems
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… 



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