Rotation Numbers of Elements in Thompson's Group ${\bf T}$

TL;DR

This paper provides a straightforward combinatorial proof demonstrating that every element in Thompson's group T has a rational rotation number, clarifying a fundamental property of these group elements.

Contribution

It introduces a simple combinatorial proof establishing the rationality of rotation numbers for all elements in Thompson's group T.

Findings

All elements in Thompson's group T have rational rotation numbers.

The proof simplifies understanding of the dynamical properties of T.

Provides a new combinatorial approach to analyzing rotation numbers.

Abstract

We give a simple combinatorial proof that the rotation number for each element in Thompson's group ${\bf T}$ is rational.