Rigid systems of second-order linear differential equations
Representation Theory
2007-10-04 v1 Classical Analysis and ODEs
Abstract
We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t), u(t)=Udy(t)/dt+Vy(t)+Pv(t) with nonsingular S and P to each system obtained from it by a small enough perturbation of its matrices A,B,C. We prove that there exists a rigid system if and only if m<n(1+square_root{5})/2, and describe all rigid systems.
Cite
@article{arxiv.0710.0862,
title = {Rigid systems of second-order linear differential equations},
author = {M. Isabel Garcia-Planas and M. Dolors Magret and Vladimir V. Sergeichuk and Nadya A. Zharko},
journal= {arXiv preprint arXiv:0710.0862},
year = {2007}
}
Comments
22 pages