On invariant control sets for control systems on $S^3$

TL;DR

This paper explores the Lie-theoretic structure of SO(1,4) and characterizes its invariant control sets on the sphere S^3, providing insights into control systems on this manifold.

Contribution

It explicitly describes the invariant control sets of certain SO(1,4) control systems on the sphere S^3 using Lie theory.

Findings

Explicit description of invariant control sets on S^3

Analysis of control systems derived from vector fields in SO(1,4)

Application of Lie-theoretic methods to control set characterization

Abstract

In this paper we describe the Lie-theoretic structure of ${\rm SO}(1,4)$ and consider control systems given by certain vector fields of ${\rm SO}(1,4)$. Then we explicitly describe its invariant control sets in the unique ${\rm SO}(1,4)$-flag manifold, namely the sphere $S^3$.