# The fundamental matrix solution corresponding to 2 is

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Unformatted text preview: at, if . A trajectory that starts at an initial time and ends at time may be decomposed into two parts. The first from time to time and the second from time to time . Mathematically, satisfies . Then and . Suppose that has period and consider the solution of [3] with matrix is the solution of the initial value problem after one period . The monodromy . Then the solution of [2] with after one period is . Consider the trajectory during the second period. It is the solution of the initial value problem . Define a new time variable , and use to see that this is the same as [2] with and replaced by . Therefore the solution of [2], with , after two periods is . After periods . The eigenvalues of are the Floquet multipliers. Suppose the initial condition =0, is also an eigenvector of and is the corresponding eigenvalue. Then , of [2], with 14 Chapter 2 part B where is the corresponding Floquet exponent. Meiss discusses the fact that the monodromy matrix is nonsingular; see Theorem 2.11. Therefore the Floquet multipliers are all nonzero and...
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