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dc.contributor.authorJorba, Angel
dc.contributor.authorRamírez Ros, Rafael
dc.contributor.authorVillanueva Castelltort, Jordi
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractLet 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.
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshDifferential equations
dc.subject.lcshGlobal analysis (Mathematics)
dc.subject.otherquasiperiodic Floquet theorem
dc.subject.otherquasiperiodic perturbations
dc.subject.otherreducibility of linear equations
dc.titleEffective reducibility of quasiperiodic linear equations close to constant coefficients
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacVarietats (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34A General theory
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject.amsClassificació AMS::58 Global analysis, analysis on manifolds
dc.rights.accessOpen Access

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