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Title: Effective Reducibility of Quasi-Periodic Linear Equations close to Constant Coefficients
Author: Jorba i Monte, Àngel
Ramírez-Ros, Rafael
Villanueva, 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:
It is part of: SIAM Journal on Mathematical Analysis, 1997, vol. 28, num. 1, p. 178-188
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ISSN: 0036-1410
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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