Abstract:
We consider a standard-like/Froeschlè map under conservative and weakly dissipative perturbations. We study the Lindstedt series (formal power series in the parameter of perturbation $\epsilon$) for lower dimensional tori. Both in the conservative and weakly dissipative case we show that, under some mild non-degeneracy conditions, there are (at least two) formal Lindstedt series defined to all orders and that they are Gevrey. Furthermore, we compute numerically the formal expansions and use them to estimate the shape of the domain of analyticity, in $\epsilon$, of the lower dimensional tori. The computations support conjectures in the literature about the domain of analyticity. Joint work with R. de la Llave.
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