Català   Castellano   English
 Empreu aquest identificador per citar o enllaçar aquest ítem: http://hdl.handle.net/2117/901

Arxiu Descripció MidaFormat
 Títol: On quasiperiodic perturbations of elliptic equilibrium points Autor: Jorba, Angel ; Simó Torres, Carlos Data: 1995 Tipus de document: Article Resum: 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. URI: http://hdl.handle.net/2117/901 Apareix a les col·leccions: EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revista Comparteix: