Jorba i Monte, ÀngelRamírez-Ros, RafaelVillanueva, Jordi2016-02-082016-02-081997-010036-1410https://hdl.handle.net/2445/69315Let 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 quasi-periodic (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 a reduction is also quasi-periodic with the same basic frequencies as Q. The results are illustrated and discussed in a practical example.11 p.application/pdfeng(c) Society for Industrial and Applied Mathematics., 1997Anàlisi global (Matemàtica)Global analysis (Mathematics)info:eu-repo/semantics/article5886822016-02-08info:eu-repo/semantics/openAccess