 9514 Jorba A., RamirezRos R., Villanueva J.
 Effective Reducibility of Quasiperiodic Linear Equations close to
Constant Coefficients
(40K, LaTeX)
Jan 19, 95

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Abstract. Let us consider the differential equation
$$
\dot{x}=(A+\varepsilon Q(t,\varepsilon))x, \;\;\;\;
\varepsilon\le\varepsilon_0,
$$
where $A$ is an elliptic constant matrix and $Q$ depends on time in a
quasiperiodic (and analytic) way. It is also assumed that the
eigenvalues of $A$ and the basic frequencies of $Q$ satisfy a
diophantine condition. Then it is proved that this system can be
reduced to
$$
\dot{y}=(A^{*}(\varepsilon)+\varepsilon R^{*}(t,\varepsilon))y,
\;\;\;\; \varepsilon\le\varepsilon_0,
$$
where $R^{*}$ is exponentially small in $\varepsilon$, and
the linear change of variables that performs such reduction is
also quasiperiodic with the same basic frequencies than $Q$.
The results are illustrated and discussed in a practical example.
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