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Normal fundamental system of solutions

From Encyclopedia of Mathematics
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of a linear homogeneous system of ordinary differential equations

A fundamental system of solutions such that any other fundamental system satisfies the inequality

here

is the Lyapunov characteristic exponent of a solution . Normal fundamental systems of solutions were introduced by A.M. Lyapunov [1], who proved that they exist for every linear system

where is a mapping

that is summable on every segment and satisfies the additional condition

References

[1] A.M. Lyapunov, "Collected works" , 1–5 , Moscow-Leningrad (1956) (In Russian)
How to Cite This Entry:
Normal fundamental system of solutions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_fundamental_system_of_solutions&oldid=48014
This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article