dc.contributor.author Jorba, Angel dc.contributor.author Simó Torres, Carlos dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2007-05-07T15:16:34Z dc.date.available 2007-05-07T15:16:34Z dc.date.created 1995 dc.date.issued 1995 dc.identifier.uri http://hdl.handle.net/2117/901 dc.description.abstract This work focusses on quasiperiodic time-dependent perturbations of ordinary differential equations near elliptic equilibrium points. This means studying $$\dot{x}=(A+\varepsilon Q(t,\varepsilon))x+\varepsilon g(t,\varepsilon)+ h(x,t,\varepsilon),$$ where $A$ is elliptic and $h$ is ${\cal O}(x^2)$. It is shown that, under suitable hypothesis of analyticity, nonresonance and nondegeneracy with respect to $\varepsilon$, there exists a Cantorian set ${\cal E}$ such that for all $\varepsilon\in{\cal E}$ there exists a quasiperiodic solution such that it goes to zero when $\varepsilon$ does. This quasiperiodic solution has the same set of basic frequencies as the perturbation. Moreover, the relative measure of the set $[0,\,\varepsilon_0]\setminus{\cal E}$ in $[0,\,\varepsilon_0]$ is exponentially small in $\varepsilon_0$. The case $g\equiv 0$, $h\equiv 0$ (quasiperiodic Floquet theorem) is also considered. Finally, the Hamiltonian case is studied. In this situation, most of the invariant tori that are near the equilibrium point are not destroyed, but only slightly deformed and shaken" in a quasiperiodic way. This quasiperiodic shaking" has the same basic frequencies as the perturbation. dc.format.extent 34 dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject.lcsh Differential equations dc.subject.lcsh Global analysis (Mathematics) dc.subject.other quasiperiodic perturbations dc.subject.other elliptic points dc.subject.other quasiperiodic solutions dc.subject.other small divisors dc.subject.other quasiperiodic Floquet theorem dc.subject.other KAM theory dc.title On quasiperiodic perturbations of elliptic equilibrium points dc.type Article dc.subject.lemac Equacions diferencials ordinàries dc.subject.lemac Varietats (Matemàtica) dc.contributor.group Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions dc.subject.ams Classificació AMS::34 Ordinary differential equations::34C Qualitative theory dc.subject.ams Classificació AMS::58 Global analysis, analysis on manifolds dc.rights.access Open Access
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