KAM for gravity water waves in finite depth (Q1650239)

Summary: We present the recent result in [the authors, ``Time quasi-periodic gravity water waves in finite depth'', Preprint, \url{arXiv:1708.01517}] concerning the existence of Cantor families of small amplitude, linearly stable, time quasi-periodic standing water wave solutions -- i.e. periodic and even in the space variable \(x\) -- of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure.