Approximating Diffeomorphisms by Elements of Thompson's Groups F and T

TL;DR

This paper demonstrates how to approximate smooth transformations of intervals and circles using Thompson's groups F and T, connecting discrete group actions with continuous dynamical systems.

Contribution

It introduces methods to approximate diffeomorphisms with elements of Thompson's groups, bridging discrete algebraic structures and continuous dynamics.

Findings

Successful approximation of diffeomorphisms by Thompson's groups

Relevance to Jones' continuum limit in quantum systems

Potential applications in dynamical systems analysis

Abstract

We show how to approximate diffeomorphisms of the closed interval and the circle by elements of Thompson's groups $F$ and $T$, respectively. This is relevant in the context of Jones' continuum limit of discrete multipartite systems and its dynamics.