E pluribus unum: natural boundaries and uniqueness in small divisor problems

Stefano Marmi  (Scuola Normale Superiore di Pisa)

Addressing a question raised by Kolmogorov and Herman, I will review previous work on the analytic structure in the complex frequency plane of solutions of certain small divisor problems and its relation with with the notion of quasianalytic function of a complex variable. I will discuss both the linear and nonlinear case.Most of the talk will be based on papers with C. Carminati, D. Sauzin and A. Sorrentino