Rigidity of Mather's $\beta$-function on a KAM set for analytic billiards-like maps and unique quasi-analytic continuation

Corentin Fierobe, Vadim Kaloshin, Frank Trujillo

In his seminal paper, Kac famously asked whether "one can hear the shape of a drum" - that is whether the isometry class of a bounded domain in a Euclidean space is uniquely determ…