A note on KAM for gravity-capillary water waves

Abstract

We present the result and the ideas of the recent paper [8] (obtained in collaboration with M. Berti) concerning the existence of Cantor families of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean, with infinite depth, in irrotational regime, under the action of gravity and surface tension at the free boundary. These quasi-periodic solutions are linearly stable.