**abstract:**
Formal power series naturally arise when considering dynamical systems with small divisors problems in the perturbative setting. I will focus on the following examples: lower-dimensional tori in quasi-integrable systems and quasi-periodic solutions in strongly damped one-dimensional systems in the presence of a
quasi-periodic forcing. The formal power series in the perturbation parameter can be given a meaning by a suitable summation rule. This leads to quasi-periodic solutions analytic in a domain tangent to the origin. In certain cases the summation rule can be proved to correspond to Borel summability.

Tue 24 Apr, 11:00 - 12:00, Sala Conferenze Centro De Giorgi

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