Floquet Theory for Quaternion-valued Differential Equations
Classical Analysis and ODEs
2020-09-29 v1
Abstract
This paper describes the Floquet theory for quaternion-valued differential equations (QDEs). The Floquet normal form of fundamental matrix for linear QDEs with periodic coefficients is presented and the stability of quaternionic periodic systems is accordingly studied. As an important application of Floquet theory, we give a discussion on the stability of quaternion-valued Hill's equation. Examples are presented to illustrate the proposed results.
Cite
@article{arxiv.1902.09800,
title = {Floquet Theory for Quaternion-valued Differential Equations},
author = {Dong Cheng and Kit Ian Kou and Yong Hui Xia},
journal= {arXiv preprint arXiv:1902.09800},
year = {2020}
}