  In the present contribution, we first prove the existence of
$\mathbf{m}$-fold simply-connected V-states close to the unit disc for
Euler-$\alpha$ equations. These solutions are implicitly obtained as
bifurcation curves from the circular patches. We also prove the existence of
quasi-periodic in time vortex patches close to the Rankine vortices provided
that the scale parameter $\alpha$ belongs to a suitable Cantor-like set of
almost full Lebesgue measure. The techniques used to prove this result are
borrowed from the Berti-Bolle theory in the context of KAM for PDEs.

Analysis of PDEs