 05399 Michele V. Bartuccelli, Jonathan H.B. Deane, and Guido Gentile
 Globally and locally attractive solutions for quasiperiodically forced systems
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Nov 23, 05

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Abstract. We consider a class of differential equations, $\ddot x + \gamma \dot x + g(x) = f(\omega t)$, with $\omega \in {\bf R}^{d}$, describing onedimensional dissipative systems subject to a periodic or quasiperiodic (Diophantine) forcing. We study existence and properties of the limit cycle described by the trajectory with the same quasiperiodicity as the forcing. For $g(x)=x^{2p+1}$, $p\in {\bf N}$, we show that, when the dissipation coefficient is large enough, there is only one limit cycle and that it is a global attractor. In the case of other forces, including $g(x)=x^{2p}$ (with $p=1$ describing the varactor equation), we find estimates for the basin of attraction of the limit cycle.
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