IJPAM: Volume 72, No. 3 (2011)

CONSTELLATION PROBLEMS AND INTEGRABILITY
FOR LINEAR ODE'S WITH CONSTANT COEFFICIENTS

Benno Fuchssteiner$^1$, Kai Gehrs$^2$
$^1$Rheinsbergerstrasse 50,
D 10435, Berlin, GERMANY
e-mail: bf@fuchssteiner.de
$^2$Department of Mathematics
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