Some problems of the linear theory of systems of ordinary differential equations |
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Authors: | A M Samoilenko |
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Institution: | (1) W. K. Kellogg Biological Station, Michigan State University, Hickory Corners, East Lansing, MI 49060, USA |
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Abstract: | We consider problems of the linear theory of systems of ordinary differential equations related to the investigation of invariant
hyperplanes of these systems, the notion of equivalence for these systems, and the Floquet–Lyapunov theory for periodic systems
of linear equations. In particular, we introduce the notion of equivalence of systems of linear differential equations of
different orders, propose a new formula of the Floquet form for periodic systems, and present the application of this formula
to the introduction of amplitude–phase coordinates in a neighborhood of a periodic trajectory of a dynamical system. |
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