Rigid systems of second-order linear differential equations

Details Rigid systems of second-order linear differential equations Rigid systems of second-order linear differential equations

2007-10-03

arxiv.org/abs/0710.0862v1

Linear Algebra Appl. 414 (2006) 517--532

Mathematics

Representation Theory

22 pages

Scientific paper

10.1016/j.laa.2005.10.037

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

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