Floquet Theory for Linear Differential Equations with Meromorphic Solutions

R. Weikard, University of Alabama, Birmingham, Alabama, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 8. (2000), pp. 1-6.

Abstract: If $A$ is a $\omega$-periodic matrix Floquet's theorem states that the differential equation $y'=A y$ has a fundamental matrix $P(x)\exp(J x)$ where $J$ is constant and $P$ is $\omega$-periodic, i.e., $P(x)=P^*(\e^{2\pi ix/\omega})$. We prove here that $P^*$ is rational if $A$ is bounded at the ends of the period strip and if all solutions of $y'=A y$ are meromorphic. This version of Floquet's theorem is important in the study of certain integrable systems.

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