We prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.

中文翻译：

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恒定涡旋传播的准周期水波

我们证明了空间周期性水波具有涡度的时间准周期行波解的第一个分叉结果。特别地，我们证明了对于由空间-周期自由界面界定的平坦底部上的二维流体，具有恒定涡度的重力-毛细管水波方程的小振幅时间准周期解的存在。这些准周期解对于深度，重力和涡度的所有值均存在，并将表面张力限制为渐近完全勒贝格测度的Borel集。