Effective reducibility of quasiperiodic linear equations close to constant coefficients
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hdl:2117/948
Tipus de documentArticle
Data publicació1995
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
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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