Scaling, perturbative renormalization and analyticity for the standard map and some generalizations

We summarize some numerical works on the analyticity properties of the perturbative series (e.g. Lindstedt series) for some simple discrete-time Hamiltonian systems like the so-called ‘standard map’ and generalizations. We stress the relevance of our results for the development of a renormalization group picture based on perturbation theory.