On invariant manifolds of linear differential equations. I

Details On invariant manifolds of linear differential equations. I On invariant manifolds of linear differential equations. I

2010-06-29

arxiv.org/abs/1006.5617v2

Mathematics

Classical Analysis and ODEs

in Ukrainian, added English translation

Scientific paper

This article is the first in the cycle from two parts. It develops the ideas of integral manifolds method of M. M. Bogolubov in the case of linear differential equations in $R^m$ with variable coefficients. We distinguish linear subspaces $M^n(t)$ and $M^{m-n}(t)$, which have dimensions $n$ and $m-n$ respectively, $m > n$, such that $R^m = M^n(t) \oplus M^{m-n}(t)$, and find necessary and sufficient conditions under which these subspaces are invariant with respect to differential equation under consideration.

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