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REDUCIBILITY OF NONAUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  24 March 2003

STEFAN SIEGMUND
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332, USA; siegmund@math.gatech.edu
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Abstract

A linear autonomous system of differential equations $\dot{x}=Ax$ can be transformed to its Jordan normal form, that is, the transformed system is in block diagonal form and the blocks correspond to different eigenvalues. This result is generalized to arbitrary nonautonomous linear systems $\dot{x}=A(t)x$ with a locally integrable matrix function $A:{\bb R}\longrightarrow {\bb R}^{N\times N}$ .

Type
Research Article
Copyright
The London Mathematical Society, 2002

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