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arXiv · 0710.0862

Rigid systems of second-order linear differential equations

M. Isabel Garcia-Planas·M. Dolors Magret·Vladimir V. Sergeichuk·Nadya A. Zharko
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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.

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M. Isabel Garcia-Planas, M. Dolors Magret, Vladimir V. Sergeichuk, Nadya A. Zharko. 2007-10-03. Rigid systems of second-order linear differential equations. https://doi.org/10.1016/j.laa.2005.10.037

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