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Floquet's Theorem

Folkers, Eline (2018) Floquet's Theorem. Bachelor's Thesis, Mathematics.


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For a homogeneous system of differential equations with a constant coefficient matrix, the fundamental matrix can be computed by using the eigenpairs of the coefficient matrix. However, for a homogeneous system of differential equations with a periodic coefficient matrix, another approach is needed to obtain the fundamental matrix. Floquet's theorem offers a canonical form for each fundamental matrix of these periodic systems. Moreover, Floquet's theorem provides a way to transform a system with periodic coefficients to a system with constant coefficients. The monodromy matrix is very useful for stability analyses of periodic differential systems, in particular for Hill's differential equation. In this thesis, Floquet's theorem will be proven, and the aforementioned transformation and stability analyses will be discussed.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Sterk, A.E.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 06 Jul 2018
Last Modified: 06 Jul 2018 14:16

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