Abstract: As discovered by Carminati, Marmi, Sauzin, for a small analytic perturbation of the integrable standard map the usual invariant KAM solution can be extended to the complex plane as an analytic map with respect to the rotation number, and this map is defined everywhere outside a set of so-called diamonds. The authors further showed that these diamonds contain singularities of the analytic extension. We will present here how their work can be adapted to a certain class of twist billiard maps, and also how it can be interesting to investigate spectral rigidity questions in billiards.
From diamonds to length spectrum rigidity
13.01.2023 14:00 - 15:15
Organiser:
Henk Bruin, Peter Balint
Location: