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Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity Angie Ash on how states use doomsdayWe consider the gravity water waves system with a periodic one dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi periodic in time, traveling waves. This provides the first existence result of quasi periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash Moser scheme, Birkhoff normal form methods and pseudo