# name
Effective Reducibility of Quasi-Periodic Linear Equations close to Constant Coefficients

# metadata.dc.description.abstract[].value
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 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.

# metadata.dc.publisher[].value
Society for Industrial and Applied Mathematics

# metadata.dc.relation.ispartof[].value
SIAM Journal on Mathematical Analysis, 1997, vol. 28, num. 1, p. 178-188

# metadata.dc.rights[].value
(c) Society for Industrial and Applied Mathematics., 1997

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Effective Reducibility of Quasi-Periodic Linear Equations close to Constant Coefficients