IJPAM: Volume 72, No. 3 (2011)
FOR LINEAR ODE'S WITH CONSTANT COEFFICIENTS



D 10435, Berlin, GERMANY
e-mail: bf@fuchssteiner.de

University of Paderborn
D-33100, Paderborn, GERMANY
e-mail: Kai.Gehrs@math.uni-paderborn.de
Abstract. In this note we show that for each system of linear differential
equations with constant coefficients - wether or not the
characteristic polynomial of the coefficient matrix can be solved
algorithmically and symbolically - a suitable set of constants of
motion can be constructed in a purely algorithmic way. The constants
of motion are given as integrals over rational functions involving
the matrix elements and the components of the solution vectors. Thus,
these systems are integrable in the same way as systems considered in
integrability theory in the situation of the Liouville-Arnold theorem for
Hamiltonian systems.
Received: October 30, 2009
AMS Subject Classification: 34-XX, 37K05
Key Words and Phrases: linear differential equations, constants of motion, integrability
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 3