Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On invariant manifolds of linear differential equations. II   This is the continuation of previous article. For subspaces $M^n(t)$ and
$M^{n-m}(t)$ which are invariant manifolds of the differential equation under
consideration we build a change of variables which splits this equation into a
system of two independent equations. A notion of equivalence of linear
differential equations of different orders is introduced. Necessary and
sufficient conditions of this equivalence are given. These results are applied
to the Flocke-Lyapunov theory for linear equations with periodic coefficients
with a period T. In the case when monodromy matrix of the equation has negative
eigenvalues, thus reduction in $R^m$ to an equation with constant coeficcients
is possible only with doubling of reduction matrix period, we prove the
possibility of splitting off in $R^m$ of equations with negative eigenvalues of
monodromy matrix with the help of a real matrix without period doubling. For
the fundamental matrix of solutions of an equation with periodic coefficients
$X(t), X(t)=E$, we find representation $X(t)=\Phi(t)e^{Ht}\Phi^{+}(0)$ with
real rectangular matrices $H$ and $\Phi(t), \Phi(t)=\Phi(t+T)$. We bring two
applications of these results: 1) reduction of nonlinear differential equation
in $R^n$ with distinguished linear part which is periodic with period T to the
equation in $R^m, m>n$, with a constiant matrix of coefficients of the linear
part; 2) for introdusing of amplitude-phase coordinates in the neigbourhood of
periodic orbit of autonomous differential equation with separation of the
linear part with constant matrix of coefficients.

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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio