Exponentially small splitting of separatrices under fast quasiperiodic forcing
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hdl:2117/949
Tipus de documentArticle
Data publicació1997
Condicions d'accésAccés obert
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Abstract
We consider fast quasiperiodic perturbations with two frequencies
$(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum,
where $\gamma$ is the golden mean number.
The complete system has a two-dimensional invariant torus in a
neighbourhood of the saddle point. We study the splitting
of the three-dimensional invariant manifolds associated to this torus.
Provided that the perturbation amplitude is small enough with respect to
$\varepsilon $, and some of its Fourier coefficients (the ones associated
to Fibonacci numbers), are separated from zero, it is proved
that the invariant manifolds split and that the value of the splitting,
which turns out to be exponentially small with respect to $\varepsilon $,
is correctly predicted by the Melnikov function.
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