Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/69315
 Title: Effective Reducibility of Quasi-Periodic Linear Equations close to Constant Coefficients Author: Jorba i Monte, ÀngelRamírez-Ros, RafaelVillanueva, Jordi Keywords: Anàlisi global (Matemàtica)Global analysis (Mathematics) Issue Date: Jan-1997 Publisher: Society for Industrial and Applied Mathematics. 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 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. Note: Reproducció del document publicat a: http://dx.doi.org/10.1137/S0036141095280967 It is part of: SIAM Journal on Mathematical Analysis, 1997, vol. 28, num. 1, p. 178-188 Related resource: http://dx.doi.org/10.1137/S0036141095280967 URI: http://hdl.handle.net/2445/69315 ISSN: 0036-1410 Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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