Group Actions as Stroboscopic Maps of Ordinary Differential Equations

TL;DR

This paper explores how group actions can be used as stroboscopic maps for ordinary differential equations, demonstrating that the flow of the Bloch equation uniquely corresponds to an invertible map on SU(2).

Contribution

It introduces a novel approach to derive discrete maps from ODEs using invertible group actions, specifically applying it to the Bloch equation.

Findings

Flow of the Bloch equation is a unique suspension of an invertible map on SU(2)

Group actions can serve as stroboscopic maps for ODEs

Potential for new analytical tools in dynamical systems

Abstract

Discrete-time dynamical systems can be derived from group actions. In the present work possibility of application of this method to systems of ordinary differential equations is studied. Invertible group actions are considered as possible candidates for stroboscopic maps of ordinary differential equations. It is shown that flow of the Bloch equation is a unique suspension of an invertible map on the SU(2) group.