Reducible linear system
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
of ordinary differential equations
A system
 | (*) |
 |
that can be transformed into a system 
with constant coefficients by a change of variables 
, where 
is a Lyapunov transformation. If the mapping 
is continuous and periodically depends on 
, then (*) is a reducible system (Lyapunov's theorem). The system (*) is reducible if and only if there is a Lyapunov transformation 
and an operator 
such that every solution of (*) has the form
 |
(Erugin's criterion).
References
| [1] | A.M. Lyapunov, "Stability of motion" , Acad. Press (1966) (Translated from Russian) |
| [2] | N.P. Erugin, "Reducible systems" Trudy Mat. Inst. Steklov. , 13 (1946) (In Russian) |
How to Cite This Entry:
Reducible linear system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reducible_linear_system&oldid=18924
Reducible linear system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reducible_linear_system&oldid=18924
This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article