The Floquet Theory for Quasi-Periodic Linear System

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Lin Zhen-sheng. The Floquet Theory for Quasi-Periodic Linear System[J]. Applied Mathematics and Mechanics, 1982, 3(3): 327-344.

Citation:

Lin Zhen-sheng. The Floquet Theory for Quasi-Periodic Linear System[J]. Applied Mathematics and Mechanics, 1982, 3(3): 327-344.

Citation:

Lin Zhen-sheng. The Floquet Theory for Quasi-Periodic Linear System[J]. Applied Mathematics and Mechanics, 1982, 3(3): 327-344.

Abstract

In this paper we establish the Floguet theory for the quasi-periodic system where A(u₁,u₂...u_m) is an nxn periodic matrix function ofwith period 2π, and it is of C^τ, τ=(N+1)τ₀, τ₀=2(m+1), N = (1/2)n(n+l).Meanwhile, we define the characteristic exponential roots β₁,β₂,…,β_n of (0.1), and assume that where K(ω), K(ω,β)->0. k_u, i_v, are integers, all the integers k₁,k₂,…,k_m,k_m are not zero, ,rhen therequasi-periodic linear transformation, which carries (0.1) into a linear system with constant coefficients.

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